Download Strategic competition

Strategic competition
American term: Industrial organization
A better name: The economics of industry
- the study of activities within an industry,
mainly with respect to competition among
the firms in a product market.
Why is this topic important?
 The model of perfect competition is unrealistic.
- Who set the prices?
– The firms.
- Can they influence the price?
– Yes, for example if their products differ,
or if they are few.
But: difficult to find a general model of imperfect
competition.
 Many models with varying applications
- Is it smart to have a whole battery of
models?
 The predictions from the perfect-competition model do
not fit. In many industries:
- high profits
- p > MC
 Competition policy
Tore Nilssen – Strategic Competition – Theme 1 – Slide 1
The study of an industry
- few firms
- partial equilibrium
- how do the firms compete with each other?
- setting prices? quantities?
- making investments? advertising? R&D?
capacity?
- location of outlets
- what do they do to avoid competition?
- product differentiation
- entry deterrence
- predatory actions
- collusion
- merger
Various models, all with the same analytical tool:
game theory
Tore Nilssen – Strategic Competition – Theme 1 – Slide 2
What is the right model to use?
- What kind of market are we looking at?
Example: market for petrol vs. market for cars
petrol: homogeneous good
car: heterogeneous good
petrol: easy for firms to supervise each other’s prices
car: price supervision difficult
Product differentiation  weaker competition
 petrol market more competitive
Price supervision: easy to coordinate on prices
 petrol market less competitive
Both markets may have the same mark-up, but
explanations may differ.
In order to understand how firms in an industry compete
(or not), we need a catalogue of different models.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 3
Even in the study of a single industry, it may be helpful
to have different models of strategic competition in
mind.
Example: Norwegian airlines.
(source: Norwegian Competition Authority)






Predation
Entry deterrence
Non-price competition
Collusion
Merger
Consumer switching costs
Tore Nilssen – Strategic Competition – Theme 1 – Slide 4
Central concepts from game theory
 Extensive form vs. normal form
 Strategy vs. action
 Pure strategy vs. mixed strategy
 Dominated strategy
 Nash equilibrium
 Subgame-perfect equilibrium
 Repeated games
Repetition of game theory:
Tirole, secs 11.1-11.3 (for ch 9: secs 11.4-11.5)
Exercises 11.1, 11.4, 11.9.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 5
Competition in the short run
or: Static oligopoly theory
Firms make decisions simultaneously
Actions chosen from continuous action spaces
Differentiable profit functions
First-order conditions
Nash equilibrium with 2 firms:
 i  s1*, s2* 
0
si
i = 1, 2
Each firm’s decision is optimum, given the other firm’s
equilibrium decision.
The other firm’s decision is exogenous.
Thus, we can find one firm’s optimum decision given the
other firm’s choice: Best-response functions
R1(s2) is firm 1’s best-response function, defined by:
 1 R1s2 , s2 
s1
0
Tore Nilssen – Strategic Competition – Theme 1 – Slide 6
Best-response curves:
s2
R1(s2)
s2*
R2(s1)
s1*
The slope of the best-response curve:
2
s1
2
 
 1
dR1 
ds2  0
2
s1
s1 s2
1
2
 R1' s2  
 1
s1 s2
dR1

2 1
ds2
 
s12
2
 1
0
Second-order condition 
2
s1
2
 1
Therefore: sign R1’(s2) = sign
s1 s2
Tore Nilssen – Strategic Competition – Theme 1 – Slide 7
2
 1
 0:
s1 s2
An increase in s2 implies a reduction in firm 1’s payoff
from a marginal increase in s1. This implies a reduction
in firm 1’s optimum. The two firms’ choice variables are
strategic substitutes.
2
 1
 0:
s1 s2
An increase in s2 implies an increase in firm 1’s payoff
from a marginal increase in s1. This implies an increase
in firm 1’s optimum. The two firms’ choice variables are
strategic complements.
Generally, but not always:
 prices are strategic complements
 quantities are strategic substitutes
Tore Nilssen – Strategic Competition – Theme 1 – Slide 8
Price competition
A firm’s price is a short-term commitment. So a regular
picture of competition in the short run is one of
competition in prices.
Modelling is a trade-off between making a model
- simple, so that we can understand it; and
- reasonable, so that we can use it.
Let us start out with simplicity.
Two firms, homogeneous goods (perfect substitutes).
Consumers care only about price.
Market demand: D(p), D’ < 0.
Constant unit cost: c.
No capacity constraints.
Firms choose prices simultaneously and independently.
Equilibrium prices – Bertrand equilibrium.
(Joseph Bertrand, 1883)
Firm 1’s profit:
1(p1, p2) = (p1 – c)D1(p1, p2), where
D p1 , if p1  p2
1
D1 p1, p2    2 D p1 , if p1  p2
0,
if p1  p2

Tore Nilssen – Strategic Competition – Theme 1 – Slide 9
1(p1, p2) is discontinuous, because D1(p1, p2) is.
First-order approach not applicable.
Nash equilibrium:
1(p1*, p2*)  1(p1, p2*),  p1.
2(p1*, p2*)  2(p1*, p2),  p2.
Result: There exists a unique equilibrium, in which
p1* = p2* = c
Two steps in the proof.
Step 1: This is an equilibrium.
Step 2: No other price combination is an equilibrium.
p2
(ii)
(i)
(iii)
(iv)
p1
c
[Exercise 5.1: cost asymmetry]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 10
The same result holds for any number of firms  2.
So there is nothing between monopoly and perfect
competition (the Chicago school).
Or is there?
The model lacks realism.
Resolving the Bertrand paradox
(i)
Product differentiation
Consumers care for both price and product
characteristics.
No longer true that R(c) = c.
If p2 = c, then p1 = c +  provides firm 1 with positive
profit.
Thus, p = c no longer equilibrium.
[Theme 3]
(ii)
Time horizon
Consider the case p1 = p2 > c. Not an equilibrium,
because firm 1 is better off with reducing its price strictly
below p2. But what if firm 2 can respond to this? Would
it set a price even lower? If so, could it be that firm 1
does not have incentives for a price reduction to start
with?
[Theme 2]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 11
(iii)
Capacity constraints
Firms cannot sell more than they are able to produce.
Capacity constraints: q1 and q 2 .
Suppose q1 < D(c).
p = c is no longer equilibrium
Suppose firm 1’s price is p1 = c. If now firm 2 sets p2 = c
+ , then firm 1 faces a higher demand than its capacity.
Some consumers will have to go to the high-price firm 2,
who therefore earns a profit.
Capacity constraints are an extreme version of
decreasing returns to scale.
[Next slides]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 12
Price competition with capacity constraints
Consumers are rationed at the low-price firm. But who
are the rationed ones?
As before: two firms; homogeneous goods.
Efficient rationing
If p1 < p2 and q1 < D(p1), then the residual demand facing
firm 2 is:
~
D p2   q1, if D p2   q1,
D2  p2   
otherwise
0,
D(p)
p2
p1
q2

q1
This is the rationing that maximizes consumer surplus:
The consumers with the highest willingness to pay get
the low price.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 13
Proportional rationing
Let p1 < p2 and q1 < D(p1).
Instead of favouring the consumers with the highest
willingness to pay, all consumers have the same chance
of getting the low price.
Probability of being supplied by the low-price firm 1 is:
q1
D p1 
The residual demand facing the high-price firm 2 is:

~
q1 

D2  p2   D p2 1
D p1 

D(p)
p2
p1

q1
Not efficient – some consumers get supplies despite
having a willingness to pay below p2, consumers’
marginal cost.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 14
q2
Example
Two firms, homogeneous demand: D(p) = 1 – p
Zero marginal costs of production: c = 0.
High investment costs have led to low capacity:
q1  q2  1 .
3
Assume efficient rationing.
Define: p* = 1 – q 1  q2 . [Note: p* ≥
1
3
> c.]
Is p1 = p2 = p* an equilibrium?
Note that D(p*) = q 1  q2 ; total capacity exactly covers
demand at this price.
Can another price be preferable for firm 1 to p*, if firm 2
sets p2 = p*?
(i)
Consider p1 < p2 = p*. A lower price for firm 1
without any increase in sales.
(ii)
Consider p1 > p2 = p*. Firm 1’s sales less than
before:
~
q1 = D1 p1  = D(p1) – q2 = 1 – p1 – q2
 p1 = 1 – q1 – q2
Tore Nilssen – Strategic Competition – Theme 1 – Slide 15
Profit of firm 1:
~
1 = p1 D1 p1 
Equivalently:
1 = (1 – q1 – q2 )q1
Is it profitable for firm 1 with a price above p*?
Equivalently: Is it profitable with a quantity
below q1 ?
d 1
 1 2q1  q2
dq1
d 2 1
Second-order condition:
< 0.
2
dq1
d 1
|q  q  1 2q1  q2  0
dq1 1 1
Optimum is at q1.
Thus, the optimum price for firm 1 is p*. Equivalently
for firm 2. Thus, p1 = p2 = p* in equilibrium.
Is this equilibrium unique? Yes.
Larger capacities: No equilibria in pure strategies.
[Exercise 5.2]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 16
Capacity a more long-term decision than price
Consider the following two-stage game:
Stage 1: Firms choose capacities
Stage 2: Firms choose prices
Investment costs: c0 per unit of capacity
Suppose c0 is so high that, in equilibrium, capacities will
be low. We can then make use of our analysis of the
price game: Prices equal p*.
Profit net of investment costs:
1( q1 , q2 ) = {[1 – ( q1 + q2 )] – c0} q1 .
Now, the game is equivalent to a one-stage game in
capacities where demand = total capacity = total supply.
That is, a one-stage game in quantities.
(Augustin Cournot, 1838)
With efficient rationing and a concave demand function,
the two games are equivalent in equilibrium outcome, for
all c0.
Therefore, a model of one-stage quantity competition,
with prices coming from nowhere, can be understood as
a simple substitute for a more realistic but more complex
model where firms compete in capacities and thereafter
in prices.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 17
The Cournot model
Two firms choose quantities simultaneously.
Costs: Ci(qi)
Total production: Q = q1 + q2
Inverse demand: P(Q), P’ < 0.
Profit, firm 1:
1(q1, q2) = q1P(q1 + q2) – C1(q1).
First-order condition:
 1
= P(q1 + q2) + q1P’(q1 + q2) – C1’(q1) = 0
q1
q1P’(q1 + q2)
–
the infra-marginal effect of an
increase in quantity
 1
 2
Equilibrium:
= 0;
= 0.
q1
q2
Tore Nilssen – Strategic Competition – Theme 1 – Slide 18
For firm 1:
P – C1’ = – q1P’ = 

P C1'

P
q1
P' Q  
Q
q1
Q
1 1
P' Q
q1
Q
1 P

P' Q
L1 =
P C1'
P
–
the Lerner index of firm 1
1 =
q1
Q
–
firm 1’s market share
–
the market demand
D(p)
D(P(Q))  Q
 D’(p) P’(Q) = 1
Demand elasticity:
1P
P
   D'  
D
P' Q
 L1 =
Note:
1

(i) 1/ > 0  L1 > 0  P > C1’.
(ii) Monopoly: 1 = 1, and L1 = 1/.
Tore Nilssen – Strategic Competition – Theme 1 – Slide 19
n firms: Q  in1 q i
i(q1, …, qn) = qiP(Q) – Ci(qi)
 i
dQ
 PQ   qi P'
 Ci '  0
qi
dq
i
1
Example: P(Q) = a – Q;
Ci(qi) = C(qi) = cqi, where a > c.
First-order condition firm i: a – Q – qi – c = 0.
All firms identical  q1 = … = qn = q, Q = nq
Applied to the first-order condition:
a – nq – q – c = 0
a c
q
n 1
na c  a  nc
a c
P = a – nq = a 

c
c
n 1
n 1
n 1
n
Q = nq =
a c
n 1
2
 a c 
a c  a c 
q 
 = q c 
  cq 

n

1
n

1
n

1




n    P  c, Q  a – c,   0.
[Exercises 5.3, 5.4, 5.5]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 20
Bertrand vs. Cournot
Competing models? – No.
Firms set prices.
When capacity constraints are of little importance, the
Bertrand model is the preferred one.
When capacity constraints are present to an important
extent (decreasing returns to scale), the Cournot model is
the best choice.
Measuring concentration
A substitute for measuring price-cost margins, since
costs are unobservable.
A popular measure: the Herfindahl index.
n
RH  i 1 i2
Model: n firms, Ci(qi) = ciqi, quantity competition
Total industry profits:
i  i  i P  ci qi  i
P i qi


PQ


2
i i
D2

RH
 D'
Assume:  = 1  pD(p) = k  D(p) = k/p
 D2/(– D’) = k  i  i  k RH
The Herfindahl index is proportional to total industry
profits.
[Exercises 5.6, 5.7]
Tore Nilssen – Strategic Competition – Theme 1 – Slide 21
Dynamic oligopoly theory
Collusion – price coordination
Illegal in most countries
- Explicit collusion not feasible
- Legal exemptions
Recent EU cases
- Banking – approx. 1.7 billion Euros in fines (2013)
- Cathodic ray tubes – 1.5 billion Euros (2012)
- Gas – approx. 1.1 billion Euros in fines (2009)
- Car glass – approx. 1.4 billion Euros (2008)
Puerto Rico, US, Dec 2013: 5-year sentence for pricefixing
Tacit collusion
Hard to detect – not many cases.
Repeated interaction
Theory of repeated games
Deviation from an agreement to set high prices has
- a short-term gain: increased profit today
- a long-term loss: deviation by the others later on
Tacit collusion occurs when
long-term loss > short-term gain
Tore Nilssen – Strategic Competition – Theme 2 – Slide 1
Model
Two firms, homogeneous good, C(q) = cq
Prices in period t: (p1t, p2t)
Profits in period t: 1(p1t, p2t), 2(p1t, p2t)
History at time t: Ht = (p10, p20, …, p1, t – 1, p2, t – 1)
A firm’s strategy is a rule that assigns a price to every
possible history.
A subgame-perfect equilibrium is a pair of strategies that
are in equilibrium after every possible history: Given one
firm’s strategy, for each possible history, the other firm’s
strategy maximizes the net present value of profits from
then on.
T – number of periods
T finite: a unique equilibrium
period T: p1T = p2T = c, irrespective of HT.
period T – 1: the same
and so on
Tore Nilssen – Strategic Competition – Theme 2 – Slide 2
T infinite (or indefinite)
At period , firm i maximizes

  t   i  p1t , p2t ,
t 

1
1 r
The best response to (c, …) is (c, …).
But do we have other equilibria?
Can p > c be sustained in equilibrium?
Trigger strategies: If a firm deviates in period t, then both
firms set p = c from period t + 1 until infinity.
[Optimal punishment schemes? Renegotiation-proofness?]
Monopoly price: pm = arg max (p – c)D(p)
Monopoly profit: m = (pm – c)D(pm)
A trigger strategy for firm 1:
 Set p10 = pm in period 0
 In the periods thereafter,
 p1t(Ht) = pm, if Ht = (pm, pm, …, pm, pm)
 p1t(Ht) = c, otherwise
Tore Nilssen – Strategic Competition – Theme 2 – Slide 3
If a firm collaborates, it sets p = pm and earns m/2 in every
period.
The optimum deviation: pm – , yielding  m for one
period.
An equilibrium in trigger strategies exists if:
m
(1 +  + 2 + … )  m + 0 + 0 + …
2

1
1 1
1
21
2
The same argument applies to collusion on any price p 
(c, pm].  Infinitely many equilibria.
The Folk Theorem.
2
1
Tore Nilssen – Strategic Competition – Theme 2 – Slide 4
Collusion when demand varies
Demand stochastic.
Periodic demand is
low: D1(p) with probability ½
high: D2(p) with probability ½
D1(p) < D2(p),  p.
The demand shocks are i.i.d.
Each firm sets its price after having observed demand.
What are the best collusive strategies for the two firms?
Trigger strategies: A deviation is followed by p = c forever.
What are the best collusive prices? One price in lowdemand periods and one in high-demand periods: p1 and p2.
s(p) – total industry profit in state s when both firms set p.
With prices p1 and p2 in the two states, each firm’s
expected net present value is:
1 D2  p2 

1 D  p 
 p2  c 
V  t  0  t  1 1  p1  c  
2 2
2 2

=
=
1
[D1(p1)(p1 – c) + D2(p2)(p2 – c)]
41 
 1  p1    2  p 2 
41   
Tore Nilssen – Strategic Competition – Theme 2 – Slide 5
The best possible collusive price in state s is:
psm = arg max (p – c)Ds(p), s = 1, 2.
sm = (psm – c)Ds(psm), s = 1, 2.
If the firms can collude on these prices, then:
 1m   2m
V
4 1   
A deviation in state s receives a gain equal to: sm
For (p1m, p2m) to be equilibrium prices, we must have:
sm  ½sm + V  sm  2V
The difficulty is state 2 (high-demand), since 1m < 2m.
The equilibrium condition becomes:
 1m   2m
  2
4 1   
2
 0
 
 1m
3 m
m
2
2
0<
 1m
 2m
<1
1
2
< 0 <
2
3
Tore Nilssen – Strategic Competition – Theme 2 – Slide 6
But what if   [ 12 , 0)? Can we still find prices at which
the firms can collude?
The problem is again state 2. We need to set p2 so that
 1m   2  p2 
 2  p2   2
4 1   

  2  p2  
 1m
2  3
1
2
<
2
3


2 3
 1  2  1
So: prices below monopoly price in high-demand state –
during boom. Could even be that p2 < p1.
But is this a price war?
More realistic demand conditions:
Autocorrelation – business cycle.
Collusion most difficult to sustain just as the downturn
starts.
Haltiwanger & Harrington, RAND J Econ 1991
Kandori, Rev Econ Stud 1991
Bagwell & Staiger, RAND J Econ 1997
[Exercise 6.4]
Tore Nilssen – Strategic Competition – Theme 2 – Slide 7
Empirical studies of collusion
 the railroad cartel
- Porter Bell J Econ 1983
- Ellison RAND J Econ 1994
 collusion among petrol stations
- Slade Rev Econ Stud 1992
 collusion in the soft-drink market: prices and advertising
- Gasmi, et al., J Econ & Manag Strat 1992
 collusion in procurement auctions
- Porter & Zona J Pol Econ 1993 (road construction)
- Pesendorfer Rev Econ Stud 2000 (school milk)
Infrequent interaction
Suppose the period length doubles.
  2
Collusion feasible if:
1
1
2 
 
 0.71
2
2
Tore Nilssen – Strategic Competition – Theme 2 – Slide 8
Multimarket contact
Market A:
Frequent interaction, period length 1.
Collusion if   ½.
Market B:
Infrequent interaction, period length 2.
Collusion if 2  ½.
(How could frequency vary across markets?)
What if both firms operate in both markets?
Can the firms obtain collusion in both markets even in
cases where 2 < ½ < ?
A deviation is most profitable when both markets are open.
Deviation yields: 2m
Collusion yields:
[m/2] every period, plus
[m/2] every second period (starting today)
Collusion can be sustained if:
m
2

[1 +  +  + … ] +
2
m
2
[1 + 2 + 4 + … ]  2m
1 1
1 1

2
21  21 2
 42 +  – 2  0   
33  1
 0.59
8
Tore Nilssen – Strategic Competition – Theme 2 – Slide 9
Secret price cuts, or:
Price coordination when supervising the partners is difficult
Own demand observable
Market demand not observable
Other firms’ prices not observable
When own demand is low, is it because market demand is
low, or because partners default?
Punishment (p = c) is necessary.
But punishment forever?
Can firms coordinate prices without being able to observe
each other’s prices?
Punishment starts when one observes low demand.
Punishment phase lasts for a finite number of periods.
Even colluding firms have periods of ‘‘price wars”.
Model: Two firms; homogeneous products; MC = c.
In each period: firms set prices; consumers choose the firm
with the lowest price.
Market demand is either:
D = 0, with probability ;
D = D(p), with probability (1 - ).
Tore Nilssen – Strategic Competition – Theme 2 – Slide 10
Both firms know it if at least one firm has zero profit in a
period. Either:
- market demand is zero and both firms have zero
profit, or
- one firm has cut its price and knows that the other
firm has zero profit
Strategy:
 Start with p = pm.
 Set p = pm until (at least) one firm has zero profit.
 If this happens, then set p = c for T periods.
 After T periods, return to p = pm until (at least) one firm
has zero profit.
And so on.
Is there an equilibrium in which each firm plays this
strategy?
T must be determined.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 11
Two phases:
 Colluding phase
 Punishment phase
V+ = net present value of a firm in the colluding phase
V = net present value of a firm at the start of the
punishment phase
 m

V  1   
 V    V 
 2


V = TV+
Equilibrium condition:
V+  (1  )(m + V) + V = (1  )m + V
 m

 1   
 V    V   1    m  V 
 2





  V V

 V  1

T
m

2
m
2
Tore Nilssen – Strategic Competition – Theme 2 – Slide 12
 m

V  1   
 V     T 1V 
 2



V 
1   
m
2
1  1      T 1
1   
m

2
 1
T 1
1  1     
T

m
2
2(1  ) + (2  1)T + 1  1
The best equilibrium has the highest possible V+.
The firms’ problem:
maxT V+, such that: 2(1  ) + (2  1)T + 1  1
But: dV+/dT < 0. So we restate the problem.
min T, such that: 2(1  ) + (2  1)T + 1  1
Tore Nilssen – Strategic Competition – Theme 2 – Slide 13
T = 0 is too low – there has to be some punishment, even
under collusion:
2(1  ) + (2  1) =  < 1
And the lefthand side must be increasing in T:

d
2 1     2  1 T 1
dT

 2  1 T 1 ln
  0  

0
1
2
If   ½, then collusion is impossible: The probability of
zero market demand is too large.
If  < ½, then 2  1 < 0. But (2  1)T + 1  0 as T  .
Equilibrium condition satisfied for some T if also
2(1  )  1
All in all: Collusion can occur in equilibrium if:
 <½
1 1
 
21
T is chosen as the lowest integer that satisfies:
2(1  ) + (2  1)T + 1  1
Example:  = ¾,  = ¼. Condition: (¾)T + 1  ¼  T* = 4.
But often T* is smaller:  = 0.9,  = 0.2  T* = 2.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 14
Price rigidities
 Menu costs
 Price reactions not punishments, but attempts to regain
market share
Suppose
- a price is fixed for two periods
- firms alternate at setting price
Duopoly with alternating price setting
 A discrete price grid
 Markov strategies: strategies based only on directly
payoff-relevant information
Example: A trigger strategy is not Markov; no price from
the past has a direct effect on a firm’s profit today, only an
indirect effect, because other firms use trigger strategies.
A restriction to Markov strategies would be too strong
when moves are simultaneous. Here, moves are alternating.
Model: duopoly; each firm’s price fixed for two periods;
firm 1 sets price in odd-numbered periods (1 – 3 – 5 – …),
firm 2 in even-numbered periods (2 – 4 – 6 – …).
Tore Nilssen – Strategic Competition – Theme 2 – Slide 15
Markov reaction functions:
Let pit be the price set by firm i in period t.
Firm 1’s reaction function:
p1, 2k + 1 = R1(p2, 2k), k = 0, 1, 2, …
Firm 2’s reaction function:
p2, 2k + 2 = R2(p1, 2k + 1), k = 0, 1, 2, …
Markov perfect equilibrium: An equilibrium in Markov
reaction functions. At the start of each subgame, the firm
that makes the move chooses an optimum strategy, given
the restriction only to pay attention to payoff-relevant
information, and given the other firm’s equilibrium
strategy.
The two firms at any point in time:
‘‘the active” and ‘‘the other”
Consider the active firm’s decision today.
Suppose the other firm set the price ph last period; this is
also its price today. – We are in state h.
Vh – the active firm’s net present value in state h.
Wh – the other firm’s net present value in state h.
Tomorrow, the roles are changed.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 16
Profit per period: (own price, the other’s price)
 Vh  max  pk , ph   Wk 
k
A symmetric equilibrium: R1() = R2() = R()
Mixed strategy: A firm may be indifferent between one or
more prices, and in equilibrium, the other firm has beliefs
about which of these prices will be chosen. These beliefs
will then constitute the firm’s mixed strategy.
hk – the probability (according to the other firm’s beliefs)
that a firm in state h chooses price pk.
Note:
 hk  1
k
A symmetric equilibrium can be described by a transition
matrix: Suppose there are H possible prices.



from state h 



 11 ... ... 1H 
 .
. 


. 
 .

 =A
.
.


 H 1 ... ...  HH 

to state k
Tore Nilssen – Strategic Competition – Theme 2 – Slide 17
Equilibrium conditions
Vh   hk   pk , ph   Wk 
k
Wk   kl   pk , pl   Vl 
l
These are the values of Vh and Wk that follow from
the transition matrix A.
[Vh – (pk, ph) – Wk]hk = 0,  h, k.
Vh  (pk, ph) + Wk,  h, k.
Complementary slackness: If hk > 0, it must be
because Vh = (pk, pl) + Wk, that is, because pk
maximizes the firm’s net present value in state h.
 hk  1,
h
k
hk  0,  h, k.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 18
Example:
D(p) = 1 – p; c = 0
The price grid: ph = h , h = 0, …, 6.
6
Competitive price: p0 = 0. Monopoly price: pm = p3 = ½.
Two (symmetric Markov perfect) equilibria (at least):
1. ‘‘Kinked demand curve”: The other firm does not
follow you if you increase the price but undercuts you if
you decrease the price.
R(1) = R( 56 ) = R( 23 ) = R( 12 ) = R(0) = 12 ;
R( 13 ) = 16 ; R( 16 )  { 16 , 12 }.
 Either the game starts in state 3 and stays there, or it
ends there sooner or later (absorbing state).
 A mixed strategy in state 1 – a waiting game (‘‘war of
attrition”): Each firm is indifferent between meeting p1
with p1, and making a short-term sacrifice in order to
get the monopoly price from next period on.
 The equilibrium is sustainable only if each firm is able
to supply the whole market demand at p1 = 16 : D( 16 ) =
5
6
. In the absorbing state 3, each firm sells 12 D(p3) =
but needs to keep an excess capacity of
5
6
–
1
4
=
7
12
1
4
.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 19
2. Price war: The firms undercut each other.
R(1) = R( 56 ) = 23 ; R( 23 ) = 12 ; R( 12 ) = 13 ;
R( 13 ) = 16 ; R( 16 ) = 0; R(0)  {0, 56 }.
 Unstable prices: no absorbing state.
 Edgeworth cycle.
 Again a waiting game. But now the price jumps
beyond the monopoly price.
*
 Multiple equilibria, even when we restrict attention to
Markov strategies.
 Fewer equilibria than in an ordinary repeated game.
 p = c is no longer an equilibrium; there is always some
price collusion in equilibrium.
Tore Nilssen – Strategic Competition – Theme 2 – Slide 20
Product differentiation
How far does a market extend?
Which firms compete with each other?
What is an industry?
Products are not homogeneous.
Exceptions: petrol, electricity.
But some products are more equal to each other than to
other products in the economy. These products constitute
an industry.
A market with product differentiation.
But: where do we draw the line?
Example:
- beer vs. soda?
- soda vs. milk?
- beer vs. milk?
Tore Nilssen – Strategic Competition – Theme 3 – Slide 1
Two kinds of product differentiation
(i)
Horizontal differentiation: Consumers differ in their
preferences over the product’s characteristics.
Examples: colour, taste, location of outlet.
(ii)
Vertical differentiation: Products differ in some
characteristic in which all consumers agree what is
best. Call this characteristic quality.
(quality competition)
Horizontal differentiation
Two questions:
1. Is the product variation too large in equilibrium?
2. Are there too many variants in equilibrium?
Question 1: A fixed number of firms. Which product
variants will they choose?
Question 2: Variation is maximal. How many firms will
enter the market?
The two questions call for different models.
Tore Nilssen – Strategic Competition – Theme 3 – Slide 2
Variation in equilibrium
Will products supplied in an unregulated market be too
similar or too different, relative to social optimum?
Hotelling (1929)
Product space: the line segment [0, 1].
Two firms: one at 0, one at 1.
0
x
1
Consumers are uniformly distributed along [0, 1].
A consumer at x prefers product variant x.
Consumers have unit demand:
p
s
1
q
Tore Nilssen – Strategic Competition – Theme 3 – Slide 3
Disutility from consuming product variant y:
t(|y – x|) – ‘‘transportation costs”
Linear transportation costs: t(d) = td
Generalised prices (with firm 1 at 0 and firm 2 at 1):
p1 + tx and p2 + t(1 – x)
s – p1– tx
s – p2 – t(1 – x)
x  p1 , p2 
x
The indifferent consumer: x
s – p1 – t x = s – p2 – t(1 – x ).
 x  p1 , p2  
1 p2  p1

2
2t
[But check that: (i) 0  x  1; (ii) x wants to buy.]
Tore Nilssen – Strategic Competition – Theme 3 – Slide 4
Normalizing the number of consumers: N = 1 (thousand)
1 p2  p1

2
2t
1 p  p2
D2(p1, p2) = 1 – x =  1
2
2t
D1(p1, p2) = x =
Constant unit cost of production: c
 1  p1 , p2    p1  c  
1
2
p2  p1 
2t 
Price competition.
Equilibrium conditions:
 1
 2
 0;
0
p1
p2
FOC[1]:
 p1  c   1   1  p2  p1 = 0
t 
2 2
t
2

increased price
reduces sales

increased price
increases gain
per unit sold
FOC[1]: 2p1 – p2 = c + t
FOC[2]: 2p2 – p1 = c + t

p1* = p2* = c + t
Tore Nilssen – Strategic Competition – Theme 3 – Slide 5
 The indifferent consumer does want to buy if:
3
s  c  2t
 Prices are strategic complements:
 2 1
1
 0
p1p2 2t
Best-response function: p1 = ½(p2 + c + t)
The degree of product differentiation: t
Product differentiation makes firms less aggressive in their
pricing.
Tore Nilssen – Strategic Competition – Theme 3 – Slide 6
But are 0 and 1 the firms’ equilibrium product variants?
Two-stage game of product differentiation:
Stage 1: Firms choose locations on [0, 1].
Stage 2: Firms choose prices.
Linear vs. convex transportation costs.
 Convex transportation costs analytically tractable –
but economically less meaningful?
Assume quadratic transportation costs.
Stage 2:
Firms 1 and 2 located at a and 1 – b, a  0, b  0, a + b  1.
The indifferent consumer:
p1 + t( x – a)2 = p2 + t(1 – b – x )2
x  a 
1
p p
1  a  b   2 1
2
2t 1  a  b 
D1(p1, p2) = x , D2(p1, p2) = 1 – x

1
2
 1  p1 , p2    p1  c a  1  a  b  

p2  p1 
2t 1  a  b 
Tore Nilssen – Strategic Competition – Theme 3 – Slide 7
Equilibrium conditions:
 1
 2
 0;
0
p1
p2
FOC[1]: 2p1 – p2 = c + t(1 – a – b)(1 + a – b)
FOC[2]: 2p2 – p1 = c + t(1 – a – b)(1 – a + b)
Equilibrium:
 a b
p1  c  t 1  a  b 1 

3 

 ba
p2  c  t 1  a  b 1 

3 

 Symmetric location: a = b  p1 = p2 = c + t(1 – 2a)
 A firm’s price decreases when the other firm gets closer:
dp1
 0.
db
 Stage-2 outcome depends on locations:
p1 = p1(a, b), p2 = p2(a, b)
Stage 1:
1(a, b) = [p1(a, b) – c]D1(a, b, p1(a, b), p2(a, b))
Tore Nilssen – Strategic Competition – Theme 3 – Slide 8
 D D p D p 
d 1
p
 D1 1   p1  c  1  1 1  1 2 
da
a
 a p1 a p2 a 

 D D p 
D  p
  D1   p1  c  1  1   p1  c  1  1 2 
p1  a

 a p2 a 


0
0 
0

d 1
D D p
  p1  c ( 1  1 2 )
da
a p2 a




direct
effect;
0
strategic
effect;
0
Moving toward the middle:
A positive direct effect vs. a negative strategic effect.
1
D1 1
p2  p1
ba
 


a 2 2t 1  a  b 2 2 31  a  b 
3  5a  b
1
 0, if a 
61  a  b 
2
p2 2
 t a  2  < 0
a 3
D1
1
>0

p2 2t 1  a  b 

D1 D1 p2 3  5a  b
a2
3a  b  1




0
a p2 a 61  a  b  31  a  b 
61  a  b 
Equilibrium: a* = b* = 0.
Tore Nilssen – Strategic Competition – Theme 3 – Slide 9
Strategic effect stronger than direct effect.
Maximum differentiation in equilibrium.
Social optimum:
No quantity effect. Social planner wants to minimize total
transportation costs. (Kaldor-Hicks vs. Pareto)
In social optimum, the two firms split the market and locate
in the middle of each segment: ¼ and ¾.
In equilibrium, product variants are too different.
 Crucial assumption: convex transportation costs.
 Also other equilibria, but they are in mixed strategies.
[Bester et al., ‘‘A Noncooperative Analysis of Hotelling’s
Location Game”, Games and Economic Behavior 1996]
 Multiple dimensions of variants: Hotelling was almost
right
[Irmen and Thisse, ”Competition in multi-characteristics spaces:
Hotelling was almost right”, Journal of Economic Theory 1998]
 Head-to-head competition in shopping malls: Consumers
poorly informed?
[Klemperer, “Equilibrium Product Lines”, AER 1992]
Have we really solved the problem whether or not the
equilibrium provision of product variants has too much or
too little differentiation?
Tore Nilssen – Strategic Competition – Theme 3 – Slide 10
Too many variants in equilibrium?
A model without location choice.
Focus on firms’ entry into the market.
The circular city
Circumference: 1
Consumers uniformly distributed around the circle.
Number of consumers: 1
Linear transportation costs: t(d) = td
Unit demand, gross utility = s
Entry cost: f
Unit cost of production: c
Profit of firm i:
i = (pi – c)Di – f, if it enters,
0,
otherwise
Tore Nilssen – Strategic Competition – Theme 3 – Slide 11
Two-stage game.
Stage 1: Firms decide whether or not to enter. Assume
entering firms spread evenly around the circle.
Stage 2: Firms set prices.
If n firms enter at stage 1, then they locate a distance 1/n
apart.
Stage 2: Focus on symmetric equilibrium.
If all other firms set price p, what then should firm i do?
Each firm competes directly only with two other firms: its
neighbours on the circle.
x in each direction is an indifferent
At a distance ~
consumer:
1

pi  t~
x  p  t  ~
x
n

1
t

~
x   p   pi 
2t 
n

Demand facing firm i:
1 p  pi
Di(pi, p) = 2 ~
x = 
n
t
Tore Nilssen – Strategic Competition – Theme 3 – Slide 12
Firm i’s problem:
 1 p  pi 
max  i   pi  c  
 f
pi
n
t


1
 i  1 p  pi 
 
   pi  c   0
pi  n
t 
t
2 pi  p  c 
t
n
In a symmetric equilibrium, all prices are equal.  pi = p.
pc
t
n
Stage 1:
How many firms will enter?
Di =
1
n
1
n
 i   p  c  f 
=0 n
 p=c+
t
f
n2
t
f
t
= c + tf
t f
Tore Nilssen – Strategic Competition – Theme 3 – Slide 13
Condition: Indifferent consumer wants to buy:
4
t
3
2
s p
=c+
tf  f  s  c 
9t
2n
2
Exercise 7.3: What if transportation costs are quadratic?
[Exercise 7.4: What if fixed costs are large?]
Social optimum: Balancing transportation and entry costs.
t 1 t
1
=
Average transportation cost: t ( ~
x)=
2 2n 4n
2
The social planner’s problem:
t 

min nf  
n 
4n 
1
t
FOC: f  2  0  n* =
2
4n
t
< ne
f
Too many firms in equilibrium.
Private motivation for entry: business stealing
Social motivation for entry: saving transportation costs
[Exercise: What happens with ne/n* as N (number of consumers) grows?]
Tore Nilssen – Strategic Competition – Theme 3 – Slide 14
Advertising
 informative
 persuasive
Persuasive: shifting consumers’ preferences?
Focus on informative advertising.
Hotelling model, two firms fixed at 0 and 1, consumers
uniformly distributed across [0,1], linear transportation
costs td, gross utility s.
A consumer is able to buy from a firm if and only if he has
received advertising from it.
i – fraction of consumers receiving advertising from firm i
Advertising costs: Ai = Ai(i) =
a 2
i
2
Potential market for firm 1: 1.
Out of these consumers, a fraction (1 – 2) have not
received any advertising from firm 2.
The rest, a fraction 2 out of 1, know about both firms.
Firm 1’s demand:

 1 p  p1 
D1 = 1 1   2    2   2

2
2
t



Tore Nilssen – Strategic Competition – Theme 3 – Slide 15
A simultaneous-move game.
Each firm chooses advertising and price.
Firm 1’s problem:

 1 p  p1  a 2
max  1   p1  c 1 1   2    2   2
  1
p1 ,1
2t  2
2

Two FOCs for each firm.


 1 p  p1 
FOC[p1]: 1 1   2    2   2
   p1  c  1 2  0
2t 
2t
2


 1 p  p1 
FOC[1]:  p1  c 1   2    2   2
  a1  0
2t 
2


p1 
1
 p2  c  t   t
2
2


1   p1  c 1   2    2  
1
a
1
2
p2  p1 

2t 
Tore Nilssen – Strategic Competition – Theme 3 – Slide 16
Firms are identical  Symmetric equilibrium
p
1
p  c  t  t
2

2 
 p  c  t   1
 
1
1
   p  c 1      
a

1 2 

  t   11  
a    2 

2
1
2a
t
Condition:
a 1

t 2
p=c+
2at
Condition: s  c + t +


 0,
a
2
2at ( c + 2t)
p
0
a
Tore Nilssen – Strategic Competition – Theme 3 – Slide 17
Firms’ profit:

2a
1  
2a
t


 0;
t
2

 0!
a
An increase in advertising costs increases firms’ profits.
Two effects of an increase in a on profits:
A direct, negative effect.
An indirect, positive effect: a     p
Firms profit collectively from more expensive advertising.
Crucial assumption: convex advertising costs.
What about the market for advertising?
[Kind, Nilssen & Sørgard, Marketing Science 2009]
Tore Nilssen – Strategic Competition – Theme 3 – Slide 18
Social optimum
Average transportation costs
among fully informed consumers: t/4.
among partially informed consumers: t/2.
The social planner’s problem:
t
t
a


max  2  s  c    2 1    s  c    2  2

4
2
2


* 
2s  c   t
3
2s  c   2a  2 t
[Condition: t  2(s – c)]
Special cases:
a
 1:
(i)
t
2
e  1
*  1 
(ii)
a
t
 :
t
<1


4 sc t
Too much advertising in equilibrium
e  0
* 
1
>0
a
1  s c
Too little advertising in equilibrium
Tore Nilssen – Strategic Competition – Theme 3 – Slide 19
Vertical product differentiation
Quality competition
Consumers agree on what is the best product variant.
But they differ in their willingness to pay for quality.
s – quality
 – measure of a consumer’s taste for quality.
If a consumer of type  buys a product of quality s at price
p, her net utility is:
U = s – p
F() – cumulative distribution function of consumer type
F(’) – fraction of consumers with type   ’.
Unit demand: If s – p  0, then a consumer of type  buys
one unit of the good.
One firm:
At price p, its demand is D(p) = 1 – F
 .
p
s
Tore Nilssen – Strategic Competition – Theme 3 – Slide 20
Two firms:
Suppose s1 < s2, p1 < p2. The indifferent consumer:
~
~
 s1 – p1 =  s2 – p2
~
 
p2  p1
s2  s1
Product 2 quality dominates product 1 if:
p
p
p
~
 < 1  2 1
s1
s2 s1
p
p 
Otherwise  2  1  , demand is:
 s2 s1 
 p  p1 
p 
 – F  1 
D1(p1, p2) = F  2
 s2  s1 
 s1 
 p  p1 

D2(p1, p2) = 1 – F  2

s
s
 2 1 
Assume:
Consumers uniformly distributed across [,  ]
Consumers sufficiently different:
 > 2
(avoiding quality dominance in equilibrium)
Firm 2 is the high-quality producer: s2 > s1.
Production costs independent of quality: c
Tore Nilssen – Strategic Competition – Theme 3 – Slide 21
Equilibrium in prices
~
 
p2  p1
s2  s1
 p  p1
 p 
Firm 1’s profit:  1   p1  c  2
 max  , 1  
 s1  
 s2  s1
Best response of firm 1:
 1 c  s1 p , if p  c   s  s 
2
1
2
 2  s2 2 
1
p1   2 c  p2   s2  s1 , if c   s1  s2   p2  c   s2  s1 

c, if p2  c   s2  s1 


p  p1 

Firm 2’s profit:  2   p2  c   2
s
s


2
1 
Best response of firm 2:
p2 
1
2
c  p1   s2  s1 
Tore Nilssen – Strategic Competition – Theme 3 – Slide 22
p2
BR1(p2)
BR2(p1)
c
c
p1
Equilibrium prices:
1
  2 s2  s1 
3
1
p2  c  2   s2  s1 
3
p1  c 
Condition for the market being covered,  
p1
:
s1
c  3 [(2s1 + s2) – ( – )(s2 – s1)]
1
Tore Nilssen – Strategic Competition – Theme 3 – Slide 23
 The high-quality firm sets the higher price:
1
p2 – p1 = 3 ( + )(s2 – s1) > 0
 The high-quality firm has the higher demand:
~ p  p1 1
1
= 3 ( + ) < 2 ( + )
  2
s2  s1
~
1
D1 =  –  = 3 ( – 2)
~ 1
D2 =  –  = 3 (2 – )
 The high-quality firm has the higher profit:
1(s1, s2) = (p1 – c)D1 = 19 ( – 2)2(s2 – s1)
2(s1, s2) = (p2 – c)D2 = 19 (2 – )2(s2 – s1)
 Firms’ profits are increasing in the quality difference
Two-stage game
Stage 1: Firms choose qualities
Stage 2: Firms choose prices
Stage 1 – feasible quality range: [s, s ]
1
Assume: c  3 [(2s + s ) – ( – )( s – s)]
In equilibrium: s1 = s, s2 = s (or the opposite).
Tore Nilssen – Strategic Competition – Theme 3 – Slide 24
 Asymmetric equilibrium
 Maximum differentiation
What if …
 c > 3 [(2s + s ) – ( – )( s – s)]
1
- the low-quality firm will choose a quality above s.
  < 2
- only one firm active in the market:
p1 = c, D1 = 0, 1 = 0
1
1
p2 = c + 2  ( s – s), D2 = 1, 2 = 2  ( s – s)
- natural monopoly: low consumer heterogeneity
makes price competition too intense for the lowquality firm
Natural duopoly for a range of consumer heterogeneity
“above”  > 2.
Vertical differentiation: the number of firms determined by
consumer heterogeneity.
Horizontal differentiation: the number of firms determined
by market size.
Tore Nilssen – Strategic Competition – Theme 3 – Slide 25
Entry
How is the market structure determined in an industry?
(number of firms, market shares, etc.)
 Entry until profit equals zero
- But what with all the positive profits we observe?
 Regulations
- But what with deregulations over the last decades?
 Technology
- Economies of scale  natural monopoly
 Vertical product differentiation
- natural oligopoly
 The established (incumbent) firms’ strategic advantage
Three strategies when confronted with an entry threat
 Blockading entry: “business as usual”
 Deterring entry: Established firms act in such a way that
entry is sufficiently unattractive
 Accommodating entry
Tore Nilssen – Strategic Competition – Theme 4 – Slide 1
Technology vs. strategic advantages
What kind of fixed costs?
 Irreversible/Sunk costs: Strategic advantage
 Reversible fixed costs: Economies of scale
Contestability theory
Main thesis: economies of scale give only a limited
advantage for the established firm
Suppose costs are:
C(q) =
cq + f,
0,
if q > 0,
otherwise
(reversible fixed costs)
D(p)
AC
pc
qc
Tore Nilssen – Strategic Competition – Theme 4 – Slide 2
The incumbent firm sets price pc and quantity qc.
This situation is sustainable in equilibrium because
- any p < pc by another firm yields a loss
- any p > pc by the incumbent firm entails entry
What game is played here?
 Prices before quantities?
 Short-term commitment of capacity; ”hit-and-run entry”.
- Short-term commitment means a small strategic
advantage.
- If another firm enters, then the incumbent wants to
leave as soon as possible.
- In order to prevent such entry, the incumbent may
want to set q > qm.
- As the commitment period shrinks to zero, q  qc.
[Tirole, pp. 340-341]
Tore Nilssen – Strategic Competition – Theme 4 – Slide 3
The strategic advantage of being incumbent
 a simple model
 a general analysis of business strategies
How to treat an entry threat? A simple model
Two-stage game: Sequential moves.
Stage 1: Incumbent (firm 1) chooses capacity.
Stage 2: Potential entrant (firm 2) chooses capacity;
zero capacity = no entry.
Profit functions (gross of any entry costs):
1(K1, K2) = K1(1 – K1 – K2)
2(K1, K2) = K2(1 – K1 – K2)
Ki = capacity choice of firm i.
 2 i
<0
K1K 2
Tore Nilssen – Strategic Competition – Theme 4 – Slide 4
Case (i): No entry costs (Stackelberg 1934)
Accommodated entry
 2
Stage 2:
= 1 – K1 – 2K2 = 0
K 2
1  K1
2
 K2 = R2(K1) =
Stage 1: 1 = K1[1 – K1 – K2] = K1[1 – K1 –
=
K1 1  K1 
2

K1s =
1  K1
]
2
1
1
1
; K 2s = R2( ) = .
2
2
4
1
8
1 = ; 2 =
1
.
16
Comparison: Simultaneous moves – Cournot.
1  K2
2
1  K1
K2 = R2(K1) =
2
1
1
 K1 = K2 = ; 1 = 2 = .
3
9
K1 = R1(K2) =
Tore Nilssen – Strategic Competition – Theme 4 – Slide 5
Case (ii): Entry costs
f = entry costs.
Entry cost not relevant for firm 1 – sunk cost.
Profit function of firm 2 net of entry costs:
2(K1, K2) = K2(1 – K1 – K2) – f,
= 0,
if K2 > 0;
if K2 = 0.
Blockaded entry: K2 = 0.
Stage 1: max 1(K1, 0) = K1(1 – K1).
1
 K1m = .
2
But when is K2 = 0 the best response to K1 =
1
?
2
1
1
Stage 2: K2 = R2( ) = , or
2
4
0.
Profit is:
1 1
2 4
2 = 2( , ) =
0.
1
– f, or
16
 Entry is blockaded if: f 
1
 0.063.
16
Tore Nilssen – Strategic Competition – Theme 4 – Slide 6
Deterred entry
Which stage-1 quantity makes firm 2 indifferent between
entry and no entry? K1b
If K1  K1b , then firm 2 chooses no entry.
Stage 2: max K2(1 – K1b – K2) – f
K2
1  K1b
.
 K2 =
2

2
max
1  K1b
1  K1b
b
]{1 – K1 – [
]} – f
=[
2
2
2
= 0  K1b  1  2 f
 max
Stage 1:
1

16
b
K1  K1m , and firm 1 prefers K1m to K1b ; blockaded entry.
f
1

16
By setting K1 = K1b , firm 1 deters entry and earns:
π1( K1b , 0) = K1b [1 – K1b ]
= (1 2 f )[1 – (1 2 f )]
= 2 f 4f
f<
Tore Nilssen – Strategic Competition – Theme 4 – Slide 7
Alternatively, firm 1 can accommodate entry and earn
(Stackelberg).
1
8
 Entry deterrence better than entry accommodation
when:
1
π1( K1b , 0) >
8
1
2 f 4f >
8
1
1
 f 
f 
0
2
32
1
1
1
 f 
f  
2
16 32
2
1
1

 f   
4  32

[We are interested in the case f < 1/16, that is,
are interested in the absolute value of

1

4
f 
1
4 2

f 
f - 1/4 < 0. Taking squares, we
f - 1/4, that is 1/4 -
f . So:
1
1 
1 
]
4
2
2
1
1 
1 3

 f 
1 
    2   0.0054
16 
2  16  2

Tore Nilssen – Strategic Competition – Theme 4 – Slide 8
 What the incumbent chooses to do in face of an entry
threat depends on the entry costs:
(i) Low entry costs imply accommodated entry:
1 3

f  [0,   2  ]
16  2

K1 = 1/2, K2 = 1/4.
(ii) Medium-sized entry costs imply deterred entry:
1 3
 1
f  (   2 , )
16  2
 16
K1 = 1 2 f , K2 = 0.
(iii) High entry costs imply blockaded entry:
1
f
16
K1 = 1/2, K2 = 0.
Tore Nilssen – Strategic Competition – Theme 4 – Slide 9
How to treat an entry threat? A more general model
Two firms:
firm 1 – the incumbent
firm 2 – the potential entrant
Stage 1:
Firm 1 chooses K1.
Firm 2 decides whether or not to enter.
Stage 2:
Either:
(i) firm 1 is a monopolist,
or:
(ii) both firms are in the market and choose their
stage-2 variables x1 and x2 simultaneously.
Stage-2 equilibrium:
{x1(K1), x2(K1)}
Comparative statics
How is stage-2 equilibrium affected by the incumbent’s
stage-1 move K1?
Can we apply comparative statics to an equilibrium?
- uniqueness
- stability
Tore Nilssen – Strategic Competition – Theme 4 – Slide 10
Stability: dynamic reasoning in a static model
If the stage-2 game changes, then also the stage-2
equilibrium changes. But will the model stabilize at the
new equilibrium?
R x 2 

1


 R2  x1 

Tore Nilssen – Strategic Competition – Theme 4 – Slide 11
Stability condition:
”R1 crosses R2 from above”
or: R1 steeper than R2, as we see them.

 
1
  R2 ' x1*
*
R1 ' x2
 
 R1’(x2*) R2’(x1*) < 1
 2 1 x1x2  2 2 x1x2
 2 1
1
2 2
2
2
   x1    x2
 2 1  2 2  2 1  2 2


0
2
2

x

x

x

x
x1 x2
1 2
1 2
Firms’ stage-2 profits:
1(K1, x1*(K1), x2*(K1)) and
2(K1, x1*(K1), x2*(K1))
What does firm 1 do at stage 1?
 If 2(K1, x1*(K1), x2*(K1))  0, then firm 1 has made a
choice of K1 at stage 1 that deters entry.
 If 2(K1, x1*(K1), x2*(K1)) > 0, then firm 1 has made a
choice of K1 at stage 1 that accommodates entry.
Tore Nilssen – Strategic Competition – Theme 4 – Slide 12
Entry deterrence
In order to deter entry, firm 1 must set K1 such that 2 = 0.
What is the effect on 2 of a change in K1?
2 = 2(K1, x1*(K1), x2*(K1))
d 2  2  2 dx1*  2 dx2*



dK1 K1 x1 dK1 x2 dK1

0
d 2  2  2 dx1*


dK1 K1 x1 dK1
 


direct
effect
strategic
effect
Stage-1 choices with a direct effect:
- location
- advertising
- not capacity
Firm 1 wants 2 so low that 2 = 0.
 If d2/dK1 < 0, then 2 = 0 is obtained by increasing K1,
that is, by being big. The strategy is to look aggressive
by being big: the top dog strategy
 If d2/dK1 > 0, then 2 = 0 is obtained by reducing K1,
that is, by being small. The strategy is to look aggressive
by being small: the lean-and-hungry-look strategy
Tore Nilssen – Strategic Competition – Theme 4 – Slide 13
Entry accommodation
The optimum choice for firm 1 at stage 1 is such that firm
2’s profit after entry is positive:
2(K1, x1*(K1), x2*(K1)) > 0
Since entry is inevitable, firm 1 seeks to maximize own
profit, given entry by firm 2.
1 = 1(K1, x1*(K1), x2*(K1))
d 1  1  1 dx1*  1 dx2*



dK1 K1 x1 dK1 x2 dK1

0
d 1  1  1 dx2*


dK1 K1 x2 dK1
 


direct
effect
strategic
effect
 1
= 0: no direct effect
Suppose
K1
Tore Nilssen – Strategic Competition – Theme 4 – Slide 14
The strategic effect
Assume firms’ stage-2 actions are symmetric: one firm’s
effect on the other firm’s profit is qualitatively the same for
the two firms.
  1 
  2 
  sign

sign


x
x
 2
 1
From the chain rule:
*
dx2* dx2* dx1*
* dx1

 R2 ' x1
dK1 dx1 dK1
dK1
 

  1 dx2* 
  2 dx1* 
  sign
  sign R2 '
sign 

x1 dK1 
x2 dK1 


slope


best strategic effect,
entry accommodation
strategic effect,
entry deterrence
response
curve
Tore Nilssen – Strategic Competition – Theme 4 – Slide 15
(i)
Stage-2 variables are strategic substitutes: R2’ < 0.
Example: quantity competition at stage 2.
  1 dx2* 
  2 dx1* 
   sign

sign


x
dK
x
dK
1
1
 2
 1
If an increase in K1 reduces 2, then it increases 1.
If an increase in K1 increases 2, then it reduces 1.
With strategic substitutes, entry accommodation and entry
deterrence are the same thing.
It is good for firm 1 to be aggressive at stage 1, also when it
accommodates entry.
The strategy is, either:
to look aggressive by being big:
the top-dog strategy,
or
to look aggressive by being small:
the lean-and-hungry-look strategy
Tore Nilssen – Strategic Competition – Theme 4 – Slide 16
Stage-2 variables are strategic complements: R2’ > 0.
Example: price competition at stage 2.
  1 dx2* 
  2 dx1* 
  sign

sign


x
dK
x
dK
1
1
 2
 1
If an increase in K1 reduces 2, then it also reduces 1.
If an increase in K1 increases 2, then it also increases 1.
An entry-accommodating incumbent firm now wants to be
non-aggressive!
If firm 1 becomes aggressive when K1 is large, then it now
wants to keep K1 down in order to look non-aggressive:
the puppy-dog strategy.
If firm 1 becomes aggressive when K1 is small, then it now
wants to have a high K1 in order to look non-aggressive:
the fat-cat strategy.
Tore Nilssen – Strategic Competition – Theme 4 – Slide 17
Business strategies
I.
Entry deterrence
Incumbent looks aggressive when investment is
II.
big
small
Top Dog
Lean and Hungry Look
Entry accommodation
Incumbent looks aggressive when
investment is
strategic
complements
strategic
substitutes
big
small
Puppy Dog
Fat Cat
Top Dog
Lean and
Hungry Look
Tore Nilssen – Strategic Competition – Theme 4 – Slide 18
Applications:
i)
Two-stage model:
1) capacities
2) prices
Prices strategic complements.
Large capacity makes a firm aggressive.
 Puppy dog strategy: Install a rather small capacity in
order to soften the ensuing price competition
ii)
Location model:
1) location
2) prices
Again: prices are strategic complements
Interpret K1 as closeness to the centre.
 Puppy dog strategy: Locate far away from the centre
in order to soften the ensuing price competition
Tore Nilssen – Strategic Competition – Theme 4 – Slide 19
iii) Puppy-dog entry
Stage 1: Entrant decides capacity and price
Stage 2: Incumbent decides price
Incumbent’s options:
 monopoly on residual market:  = A + C
 undercut and get the whole market:  = B + C
D(p) – Q
D(p)
pM
A
p2
c2
C
B
cM
xM

Q
Entrant’s optimum decision: Choose p and Q such that A > B.
[Gelman and Salop, ”Judo Economics: Capacity Limitation and Coupon Competition”,
Bell Journal of Economics 14 (1983), 315-325]
A Norwegian example: Viking Cement, 1983.
[Sørgard, ”A Consumer as an Entrant in the Norwegian Cement Market”, Journal of
Industrial Economics, 41 (1993), 191-204]
Tore Nilssen – Strategic Competition – Theme 4 – Slide 20
iv) Persuasive advertising
Stage 1: Incumbent invests in loyalty-inducing advertising
Stage 2: Price competition (if entry)
Entry deterrence: look aggressive
High investments  Many loyal firm-1 customers in stage
2  High price by firm 1
 Lean and Hungry Look: In order to deter entry, the
incumbent firm keeps its advertising low in order to keep
post-entry prices, and therefore firm 2’s post-entry profit,
low.
Entry accommodation: look non-aggressive
Firm 1 wants to have many loyal customers, so that its
incentives to set a low price in stage 2 are weak.
 Fat Cat strategy
Example: the Norwegian ice-cream market 1992
NM (Norske Meierier) vs GB.
High level of advertising by NM. Not because NM wanted
to keep GB out, but because it wanted to keep GB’s prices
high (Fat Cat).
Tore Nilssen – Strategic Competition – Theme 4 – Slide 21
Information and strategic interaction
Assumptions of perfect competition:
(i)
(ii)
agents (believe they) cannot influence the market
price
agents have all relevant information
What happens when neither (i) nor (ii) holds?
Strategic interaction among a group of firms where some or
all are incompletely informed
In particular: What happens when a firm knows more than
the others about demand, own costs, etc.?
Equilibrium outcome is now also determined by
incompletely informed firms’ beliefs. These beliefs are
represented by subjective probabilities.
(i)
Incomplete information in a static model
- how beliefs determine the equilibrium
(ii)
… in a dynamic model
- how beliefs are formed
Tore Nilssen – Strategic Competition – Theme 5 – Slide 1
Games with incomplete information
Perfect Bayesian Equilibrium:
Both strategies and beliefs are in equilibrium.
 Given the strategies in equilibrium, which revised beliefs
are consistent with these strategies?
 Given the beliefs in equilibrium, which strategies are in
equilibrium?
Two different kinds of problem:
 Asymmetric information – and the importance of the
uninformed firm observing the informed firm’s actions.
 Symmetric, incomplete information – and how there still
may be a lot of action even though firms cannot observe
each other’s actions.
Signalling
A typical signalling game:
Stage 1: The informed player chooses an action (signals)
Stage 2: The uninformed player observes stage 1, revises
his beliefs about the informed player, and chooses an action
himself.
The informed player’s private information – his type
  {High, Low}
Tore Nilssen – Strategic Competition – Theme 5 – Slide 2
The uninformed player’s beliefs about the other’s type:
Initial beliefs
Pr(High) = pH
Pr(Low) = pL = 1 – pH
Stage 2: revised beliefs
Equilibrium: actions and revised beliefs
Separating equilibrium: the action taken by the informed
player at stage 1 depends on his type.
Pooling equilibrium: the action taken by the informed
player at stage 1 is independent of his type.
In a pooling equilibrium, the uninformed player learns
nothing about the other player’s type from observing his
stage-1 action. Beliefs cannot be updated based on that
action.
In a separating equilibrium, on the other hand, the stage-1
action reveals the informed player’s type, and so, based on
that action, the uninformed player can update his beliefs
about the other player’s type and act accordingly.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 3
First – a static model:
Price competition with asymmetric information
Two firms. Product differentiation. Price competition.
Product differentiation: A slight increase in a firm’s price
causes a slight decrease in its demand and a slight increase
in the other firm’s demand.
D1 = D1(p1, p2); D2 = D2(p2, p1)
− +
– +
Firm 1 has private information about own costs.
Both firms know firm 2’s costs.
Firm 1’s unit costs:
c1 = c1L , with probability x
c1 = c1H , with probability (1 – x)
c1L < c1H
Firm 2 only knows the probability distribution ( c1L , c1H , x)
Firm 1 knows both c1 and the probability distribution.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 4
In the case of complete information:
1 = (p1 – c1)D1(p1, p2)
 1
D  p , p 
 D1  p1 , p2    p1  c1  1 1 2  0
p1
p1
Best response of firm 1: R1(p2).
Slope of the best response:
2
 1
.
sign R1’(p2) = sign
p1 p2
 2 1
D1  p1 , p2 
 2 D1  p1 , p2 

  p1  c1 
p1p2
p2
p1p2
 First term positive
 2 D1
 Slope of the best response positive unless
very
p1p2
negative.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 5
Equilibrium with complete information:
p2
R1(p2)
R2(p1)
p1
Tore Nilssen – Strategic Competition – Theme 5 – Slide 6
The optimum p1 is increasing in c1:
 2 1
 2 1
dp1 
dc1  0
p1c1
p12
dp1
 2 1 p1c1 D1 p1
 2
 2
0
2
2
dc1
  1 p1
  1 p1
p2
R1L
R1H
R2
p1
Tore Nilssen – Strategic Competition – Theme 5 – Slide 7
Firm 2 doesn’t know firm 1’s type. Firm 2 behaves as if
confronting an expected firm 1.
R1e
R1L
p2
R1H
R2
p2 *
p1L*
p1H *
p1
Analytically, we find three prices:
The price of the uninformed firm.
The price of the informed firm if it has high costs.
The price of the informed firm if it has low costs.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 8
How is the equilibrium affected by incomplete
information?
If firm 1 is low-cost, then incomplete information increases
the equilibrium prices.
If firm 1 is high-cost, then incomplete information reduces
the equilibrium prices.
Probability of firm 1 being low-cost: x
An increase in x reduces equilibrium prices, whether firm 1
is low-cost or high-cost.
If firm 1 could choose x, it would want x to be low, whether
the firm actually is low-cost or high-cost.
 The informed firm would like to be believed to have high
costs, because that would keep prices high.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 9
Dynamic model
Stage 1: An action by firm 1 that may potentially influence
firm 2’s subjective probability that firm 1 is low-cost.
Stage 2: Price competition with asymmetric information
What action?
(i)
Verifying costs – external audit
Verification is good for firm 1 if it is high-cost, but
not if it is low-cost.
(ii)
Verification not possible
Model: Two-period price competition between two firms
Period 1: Price competition
Period 2: Price competition
Is it possible for firm 2 to infer firm 1’s cost from firm 1’s
price in stage 1?
In period 1, a high-cost firm 1 would want to set a price
that reveals its cost, while a low-cost firm 1 would not want
to reveal its cost.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 10
Signalling game.
Could it be possible for a high-cost firm 1 to set a price in
period 1 that is so high that a low-cost firm 1 would not
want to mimic it?
– Yes, because increasing the price is less costly for a highcost firm than for a low-cost firm.
1 = (p1 – c1)D1(p1, p2)
 2 1
D
 1 0
p1c1
p1
The effect on firm 1’s profit of a price increase depends on
the firm’s costs. The higher costs are, the stronger is the
effect if it is positive, and the weaker is the effect if it is
negative.
1
low-cost
high-cost
p1
Tore Nilssen – Strategic Competition – Theme 5 – Slide 11
A separating equilibrium is one where firm 1’s price in
period 1 depends on its costs.
A pooling equilibrium is one where firm 1’s price in period
1 is the same whether it is low-cost or high-cost.
p2
R1L
R1H
R2
p1
If firm 1’s price in period 1 reveals its costs, then there is
complete information in period 2.
If firm 1’s price in period 1 is uninformative of its costs,
then the period-2 game is as in the static model.
Firm 1 would want firm 2 to believe it is high-cost, whether
this is true or not.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 12
Firm 2 will only believe firm 1 is a high-cost firm if it sets
a price in period 1 that is so high that a low-cost firm would
never set it – even though, by doing so, it would be
considered a high-cost firm in period 2.
Thus, in a separating equilibrium, the high-cost bestresponse curve in period 1 is further to the right than in the
static model.
Therefore, the expected best-response curve shifts to the
right, and all prices are higher in period 1 of the two-period
model than in the static model.
p2
p1
An extension: each firm has private information about own costs. The result
that prices are higher still holds.
[Mailath, ”Simultaneous Signaling in an Oligopoly Model”, Quart J Econ 1989]
High-cost firm sets high price today in order to induce a high price
tomorrow.  Puppy Dog strategy
Tore Nilssen – Strategic Competition – Theme 5 – Slide 13
Entry deterrence
Top Dog strategy
Two periods. Firm 1 has private information about own
costs.
Period 1: Firm 1 is monopolist. It cannot deter entry
through capacity investments, etc. Can it deter entry
through its period-1 price?
Firm 1 wants firm 2 to believe its costs are low.
 2
E 2
 0,
0
x
c1
The interesting case: Entry is profitable for firm 2 if firm 1
has high costs but not if it has low costs.
Reducing the price is less costly for a low-cost firm than
for a high-cost firm.
1
low-cost
high-cost
p1
Tore Nilssen – Strategic Competition – Theme 5 – Slide 14
Complete information:
Period-1 price is the monopoly price.
Incomplete information: One of two situations may occur.
(i)
Low-cost firm 1 sets a price below its monopoly
price, in order to signal its low costs.
 Separating equilibrium
(ii)
Both types of firm 1 set the low-cost monopoly
price.
 Pooling equilibrium
 Can only happen if firm 2, without any new
information, is deterred from entry.
Limit pricing: Price reduction to deter entry.
Is limit pricing credible?
In case (i), it is. The price reduction in the separating
equilibrium serves to inform the potential entrant that entry
is not profitable because of the presence of a very potent
incumbent.
In case (ii), it is not. However, the outside firm hasn’t
learned anything during period 1 and therefore chooses to
stay out.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 15
What are the welfare consequences of incomplete
information?
In both cases: Expected price lower because of incomplete
information.
In case (i) – separating equilibrium – entry behaviour is
unaffected by incomplete information. Thus, with a
separating equilibrium, incomplete information is good for
welfare.
In case (ii) – pooling equilibrium – the high-cost firm 1
manages to deter entry by mimicking the low-cost type.
Thus, incomplete information implies less entry. Total
effect on welfare is unclear.
What if the entrant does not know its own costs?
Suppose firms’ costs are the same, but only firm 1 knows
what they are.
 2
0
c
Firm 1 wants to signal high costs in order to deter entry.
Now, the high-cost firm sets price above monopoly in order
to deter entry.
Puppy Dog as entry deterrence.
[Harrington, ”Limit Pricing When the Potential Entrant Is Uncertain of Its Cost
Function”, Econometrica 1986]
Tore Nilssen – Strategic Competition – Theme 5 – Slide 16
Incomplete information and unobservable action

Rival’s price is unobservable
(recall Green & Porter)
 Incomplete information about demand
 Symmetric information: Both firms incompletely
informed
 Learning over time
- Collecting information today in order to have more
knowledge about demand tomorrow
 Strategic aspects of learning
- A firm may try to disturb the other firm’s learning
today in order to affect future decisions
Model:
Two firms. Two periods.
Product differentiation. Price competition each period.
- Prices are strategic complements.
Firms do not observe each other’s prices.
Firms do not know the market demand function.
qi = a – pi + bpj
Tore Nilssen – Strategic Competition – Theme 5 – Slide 17
 Firm A wants firm B to set a high price in period 2.
 Firm B will only set a high price in period 2 if it believes
demand is high.
 Firm B may think demand is high if it has high sales in
period 1.
 Firm A may set a high price today in order for firm B to
believe demand is high.
 But also firm B reasons the same way about firm A.
 And each firm also knows the other firm manipulates its
learning.
 Both firms set high prices in period 1 in order to
manipulate each other’s learning.
 But each firm is able to see through the other firm’s
manipulation and learns the correct demand condition
before period 2.
 Signal-jamming: manipulating others’ learning
 In our case: signal-jamming increases period-1 prices.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 18
Signal-jamming
s
observed
by the other


controlled
by the firm


stochastic
term
Other applications:
Organizational economics, corporate governance
– moral hazard
A specific model:
Firms: I and II
No costs.
Demand: Di(pi, pj) = a – pi + pj, i  j.
No firm knows a, only its expected value: ae = Ea
The one-period case: (Benchmark)
Each firm solves:


max E i  E a  pi  p j  pi   a e  pi  p j pi
pi
Best-response function: pi 
ae  p j
2
Equilibrium: pI = pII = ae.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 19
The two-period case:
Learning about a if other firm’s price is observable:
a = Di + pi – pj
But other firm’s price is not observable
D p 
ii
observed
by firm i

p
j
a
stochastic
term
controlled
by firm j
In a symmetric equilibrium, each firm sets the same price
in equilibrium, , so that: Di = a –  +  = a
But which price?
If firm II sets the price  and believes firm I does the same,
what price would firm I want to set?
Firm II’s estimate of a after period 1:
 
a~  D1II = a –  + p1I  a~  a~ p1I
In period 2, firm II believes it is playing a game of
complete information where a = a~ p1I .
 p 2  a~ p1
II
 
 
I
Tore Nilssen – Strategic Competition – Theme 5 – Slide 20
What are the incentives for firm I to set a price in period 1
that differs from ?
First, consider period 2: Firm I has been able to deduce the
true a and solves:
maxa  pI2  a~  p1I  pI2
pI2

pI2
 
a  a~ p1I
a  a    p1I
p1I  


a
2
2
2
Firm I’s period-2 profit:

p1I   
2

 I   a 
2


2
Period 1:
What is the optimum price for firm I in period 1, given firm
II’s price ?
Discount factor:   (0, 1]
Firm I solves:
2
1





p

1
1
I
 
E  a  pI   pI    a 
max
1
a
2  
pI





Tore Nilssen – Strategic Competition – Theme 5 – Slide 21
FOC: a 
e
2 p1I
 e p1I   
  0
     a 
2 

In a symmetric equilibrium: p1I = .
ae – 2 +  + ae = 0
 First-period price:  = ae(1 + )
 Manipulation of learning fails.
 The firms set higher prices in period 1 than if
manipulation of each other’s learning were not possible.
 Puppy-dog strategy: A high price today in order for the
other firm to believe demand is high and therefore set a
high price tomorrow.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 22
Strategic interaction in one market –
incomplete information in another
A version of predation:
The stronger firm competes aggressively in order to reduce
the weaker firm’s financial resources.
Product market: Duopoly – complete information
Capital market: Competitive – incomplete information
Two periods.
The two firms differ in financial strength:
The “long purse” story.
In order to operate in the market in period 2, each firm has
to incur an investment K.
Firm 1 has internal funds in excess of K.
Firm 2 has to borrow on the capital market: Its internal
funds equal E < K.
Firm 2 borrows D = K – E, and has to pay back: D(1 + r)
Interest rate: r
Tore Nilssen – Strategic Competition – Theme 5 – Slide 23
Firm 2’s gross profit in period 2 is stochastic: ~  [, ]
Cumulative distribution function: F(~ ); F’(~ ) = f(~ )
Expected value: e
If  < D(1 + r), then firm 2 goes bankrupt.
Bankruptcy:
The bank receives  and incurs bankruptcy costs B.
Competitive capital market – banks’ profits 0.
Banks’ cost of funds: r0
The interest rate in equilibrium solves:
D 1 r 
1  r D1  F D1  r    ~  B  f ~ d~  1  r0 D

The expected bankruptcy costs will have to be covered by
the borrowers.
So firm 2’s capital costs is
[(1 + r0)E] + [(1 + r0)D + BF(D(1 + r))] =
(1 + r0)K + BF((K – E)(1 + r))
Tore Nilssen – Strategic Competition – Theme 5 – Slide 24
Firm 2’s expected net profit in period 2:
W = e – (1 + r0)K – BF((K – E)(1 + r))
The higher is firm 2’s internal funds, the more likely is it
that firm 2 will undertake the period-2 investment:
An increase in E
- lowers debt K – E
- lowers interest rate r
Thus:
dW
0
dE
Period 1:
 E is a function of firm 2’s period-1 profits.
 Firm 1 can lower E by reducing prices in period 1.
 Predatory pricing.
Tore Nilssen – Strategic Competition – Theme 5 – Slide 25
Research and development (R&D)
What will a market look like in the future?
- which firms?
- which products?
- which production technology?
Depends on:
- entry deterrence
- regulation
- innovation
- …

Two kinds of innovation
 Product innovation
 Process innovation
Product innovation a special case of process innovation?
Tore Nilssen – Strategic Competition – Theme 6 – Slide 1
Process innovation
What is the value of an innovation?
- for society
- for the innovating firm
It depends on the situation.
Patents: protecting inventions
Consider a firm making an innovation that is patentprotected forever.
Constant unit costs.
The innovation reduces costs from c to c, c > c.
The value to a social planner
c
D(p
)
Vs 
1 c
 Dc dc
r c
Tore Nilssen – Strategic Competition – Theme 6 – Slide 2
The private value
(1) monopoly
(p, c) = (p – c)D(p)
pm(c) = argmaxp (p, c)
m(c) = (pm(c), c)


d m c   dp m   p m , c



= – D(pm(c))
dc
p dc
c
c
pm(c) > c,  c  D(pm(c)) < D(c),  c.
Vm 


1 c
D p m c  dc  V s

c
r
Tore Nilssen – Strategic Competition – Theme 6 – Slide 3
(2) competition
Suppose all firms in the market have constant unit costs c .
Homogeneous products. Price competition.
p = c .  = 0.
One firm makes an innovation, getting c = c.
Two cases to consider:
(i)
The innovation is drastic: pm(c)  c .
Even at the monopoly price, the innovating firm takes
the whole market.
(ii) The innovation is non-drastic: pm(c) > c .
Also now, the innovating firm takes the whole market,
but has to set p = c .
Tore Nilssen – Strategic Competition – Theme 6 – Slide 4
Consider a non-drastic innovation.
c = ( c – c)D( c )
Vc 
1
c  c Dc   1 cc Dc dc
r
r
 c > c, pm(c) > pm(c) > c
 D(pm(c)) < D( c ),  c > c.
 Vm < Vc.
D( c ) < D(c),  c < c .
 Vc < Vs
 Vm < Vc < Vs
Exercise 10.1: This ranking also holds for drastic innovations
Tore Nilssen – Strategic Competition – Theme 6 – Slide 5
Why is Vm < Vc?
The replacement effect of an innovation. (Arrow, 1962)
In the competition case, the innovating firm escapes a zeroprofit situation.
In the monopoly case, the innovating firm replaces one
monopoly situation with another one.
Because of the replacement effect, competition is good for
firms’ incentives to innovate.
Exercises 10.2, 10.3.
Tore Nilssen – Strategic Competition – Theme 6 – Slide 6
(3) a monopolist threatened by entry
Suppose the entrant innovates in case the monopolist does
not. This increases the monopolist’s incentives to innovate,
since now the alternative is worse.
d(c1, c2) – profit per period in a duopoly when own cost is
c1 and rival’s cost is c2.
If the monopolist does not innovate and the other firm
enters and does innovate, then the monopolist earns
d( c , c) and the new firm earns d(c, c ).
Assumption: m(c)  d( c , c) + d(c, c )
Value of the innovation for the monopolist:
Vm =
1 m
[ (c) – d( c , c)]
r
 Vm – Vc =
1 m
[ (c) – d( c , c) – d(c, c )]  0
r
Opposite ranking, because of the efficiency effect: a
monopolist earns more than two duopolists.
Tore Nilssen – Strategic Competition – Theme 6 – Slide 7
The two effects:
- the replacement effect
- the efficiency effect
Patent race
Two firms, incumbent and potential entrant, fight to be first
to make an innovation with an ever-lasting patent.
The more valuable the innovation is for the incumbent, the
more resources it spends on being first, and the greater is
the probability that it will win the race and get even more
control over the market.
If the efficiency effect dominates the replacement effect,
then Vm > Vc and the incumbent gets even more control
over the market.
Opposite, if Vc > Vm, then the entrant takes over, at least in
expectation.
Tirole, Sec. 10.2
Tore Nilssen – Strategic Competition – Theme 6 – Slide 8
Strategic technology adoption
Technology without patent protection.
Technology adoption is costly.
Two firms, homogeneous products.
Constant unit costs c . Zero profits.
Low-cost technology is available: c < c
Non-drastic innovation: If only one firm adopts the new
technology, then it earns c – c per unit per period.
Assume: D( c ) = 1.
c c
r
Value for non-innovating firm: 0.
Value of innovation: V =
Costs of adoption  A firm will not want to adopt if the
other one has already adopted.
Strategic incentives to adopt early. But what happens when
both know they both have such incentives?
Adoption costs are decreasing over time: C(t),
C(0) very high, C’(t) < 0, C’’(t) > 0.
Tore Nilssen – Strategic Competition – Theme 6 – Slide 9
Net present value of adopting new technology at time t,
given that none of the firms adopted before time t, is:
L(t) = [V – C(t)]e-rt
This is the value of being technology leader.
The follower does not adopt: F(t) = 0,  t.
(i)
The technology leader picked in advance –
technology adoption without strategic
considerations.
The leader maximizes L(t):




L' t     C ' t   r V  C t e rt  0
 
marginal gain marginal cost 
from delay
from delay

C(t*) = V +
(ii)
C ' t *
<V
r
Strategic considerations
Both firms consider technology adoption
Define tc by: L(tc) = 0
 C(tc) = V  tc < t*
Tore Nilssen – Strategic Competition – Theme 6 – Slide 10
A firm never adopts before tc.
The best response to the other firm’s adoption at t’ > tc is to
adopt at t  (tc, t’).
The best response to the other firm’s adoption at tc is not to
adopt at all.
The best response to the other firm not adopting is to adopt
at t* > tc.
The only possible equilibrium is one in mixed strategies.
At each point t, each firm has a subjective probability p(t)
that the other firm adopts the technology at t, given that
none of the firms has adopted so far.
In equilibrium, the firms are indifferent between adopting
and not at each t  tc.
Payoff to each firm if they both adopt at time t:
B(t) = – C(t)e-rt
Equilibrium condition:
L(t)[1 – p(t)] + B(t)p(t) = F(t)
[V – C(t)][1 – p(t)] – C(t)p(t) = 0
 p(t) = 1 –
C t 
,
V
t  tc
 A strong strategic incentive for adoption
 But what if profits are positive with competition?
- product differentiation?
Tore Nilssen – Strategic Competition – Theme 6 – Slide 11
Network externalities
Positive externalities between consumers
Example: telephone, telefax
More generally: network effects
Example: system goods, such as
- computers / software,
- DVD players / DVDs
When a new technology is available, each consumer must
decide whether to switch.
A coordination problem: the more consumers switching,
the higher is the utility for each from switching.
Excess inertia: consumers wait longer than what is socially
optimum because no-one wants to be first to switch to the
new technology.
Excess momentum: consumers switch too early because
they do not want to be left with the old technology.
On the supply side:
- which technology to offer?
- standardization of new technology
- compatibility with other products
Tore Nilssen – Strategic Competition – Theme 6 – Slide 12
A model of consumer behaviour with network externalities
Two consumers.
Two technologies: old and new.
q = network size  {1, 2}
u(q) = a consumer’s utility with old technology
v(q) = a consumer’s utility with new technology
Positive network externalities:
u(2) > u(1), v(2) > v(1)
Better to be together than separate:
u(2) > v(1), v(2) > u(1)
Consumer 1
New
Old
Consumer 2
New
Old
v(2), v(2)
v(1), u(1)
u(1), v(1)
u(2), u(2)
Two pure-strategy equilibria: {New, New} and {Old, Old}.
Excess inertia:
If the consumers play {Old, Old} and v(2) > u(2).
Excess momentum:
If the consumers play {New, New} and v(2) < u(2).
Tore Nilssen – Strategic Competition – Theme 6 – Slide 13
A more sophisticated model
Dynamic analysis: Two periods.
Incomplete information about the other consumer’s
preferences.
A consumer of type  has preferences
u(q) and v(q), q  {1, 2},   [0, 1].
The higher  is, the more interested the consumer is in
switching to new technology:
d v 2   u 1
0
d
Network externalities:
u(2) > u(1),  ;
v(2) > v(1),  .
The highest -type prefers switching even if he is alone:
v1(2) > v1(1) > u1(2) > u1(1)
The lowest -type is the opposite:
u0(2) > u0(1) > v0(2) > v0(1)
 Coordination problems only for consumer types in the
middle range.
Consumers are independently and uniformly distributed on
[0,1].
Tore Nilssen – Strategic Competition – Theme 6 – Slide 14
Four possible strategies for a consumer:
(1) Never switch
(2) Do not switch in period 1; switch in period 2
regardless of what happened in period 1.
(3) Do not switch in period 1; switch in period 2 if and
only if the other consumer switched in period 1.
(4) Switch in period 1.
Strategy (2) is dominated by strategy (4).
 Strategy (4) never fares worse than (2), and if the
opponent plays strategy (3), then strategy (4) is
strictly better than (2).
Equilibrium play depends on :
*
0
never
(1)
**
jump on the
bandwagon
(3)
1

immediately
(4)
A consumer of type * is indifferent between the old
technology with a small network and the new technology
with a big network:
u*(1) = v*(2)
Tore Nilssen – Strategic Competition – Theme 6 – Slide 15
A consumer of type ** is indifferent between:
(a) switching to a big network only if the other consumer
switched in period 1, and otherwise staying in a big
network; and
(b) switching in period 1, implying being in a small
network if the other consumer plays strategy (1) and in
a big network otherwise
v**(2)(1 – **) + u**(2)** = v**(1)* + v**(2)(1 – *)

[v**(2) – u**(2)]** = [v**(2) – v**(1)]*
 v**(2) > u**(2)
Excess inertia may occur: In the case where both
consumers have s just below **, no-one switches to the
new technology because they play the jump-on-the
bandwagon strategy, even if v(2) > u(2).
The supply side
Stage 1: Each firm decides whether its product is to be
compatible with rival firms’ products.
Stage 2: Price or quantity competition.
Trade-off: Compatibility implies a larger market, but
tougher competition.
Tore Nilssen – Strategic Competition – Theme 6 – Slide 16
Vertical relations
Products are sold through retailers.
How does this affect market performance?
c
Producer
pw
pw – wholesale price
Retailer
p
p – retail price
Demand: q = D(p)
Contracts producer-retailer
One extreme:
vertical integration –
producer and retailer act as if they are one firm
The other extreme:
linear price –
total price is T(q) = pwq
Tore Nilssen – Strategic Competition – Theme 7 – Slide 1
Two-part tariff
total price is T(q) = A + pwq
price per unit decreasing in q – quantity discount
A – franchise fee
Resale price maintenance
Producer determines the retail price.
US Supreme Court: The Leegin case (2007)
Variations: price ceiling, price floor.
Exclusive dealing
Retailer is not allowed to carry competing producers’
products.
(inter-brand competition)
Exclusive territories
Retailer has the sole right to sell the producer’s products
within a specified area.
(intra-brand competition)
Arguments for vertical integration
 the theory of the firm – Ronald Coase
 transaction costs
 incentives for relationship-specific investments
 we focus here on other arguments
Tore Nilssen – Strategic Competition – Theme 7 – Slide 2
Vertical externalities
 Double marginalization
If both producer and retailer are monopolists, then quantity
sold is less than if they were integrated.
pw > c  pm(pw) > pm(c)
Example: D(p) = 1 – p, c < 1
(i)
No integration
The retailer solves:
maxp r = (p – pw)(1 – p)
 p
1  pw
1  pw
q
2
2
The producer solves:
1  pw
max  p   pw  c 
pw
2
 pw 
1 c
3c
1 c
, q
 p
2
4
4

1  c 2 1  c 2
Total profit:  ni   p   r 

8
16

3
1  c 2
16
Tore Nilssen – Strategic Competition – Theme 7 – Slide 3
(ii)
Integration
The integrated firm solves:
maxp i = (p – c)(1 – p)
 p
Profit:  i 
1 c 3  c
1 c
, q

2
4
2
1
1  c 2   ni
4
Both the two firms and society would gain from
integration.
Alternatives to full integration
(a) two-part tariff
T(q) = A + pwq
2

1  c
The producer can set: pw = c, A 
4
Interpretation: Sell the whole business to the retailer for a
price equal to monopoly profit – the retailer becomes the
residual claimant.
But:
- risk-sharing: what if D(p) is uncertain and the retailer is
risk averse?
- asymmetric information about D(p)
Tore Nilssen – Strategic Competition – Theme 7 – Slide 4
(b) resale price maintenance
Producer restricts retail price: p  pm,
sets wholesale price: pw = pm.
But again: risk sharing
Other externalities
- retailer service
The retailer may, by putting in promotion effort, increase
the demand for the product. But some of the increase in
demand will benefit the producer.
Two-part tariff still works (but: risk sharing?)
Resale-price maintenance is not sufficient:
The producer would want to control the service level,
too.
- input substitution
Tie-in: producer sells both inputs to the retailer.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 5
A horizontal externality
Several retailers.
One retailer’s advertising effort benefits also the other
retailers.
The producer needs to encourage such efforts in order
himself to benefit from this externality.
Two-part tariff with pw < c
Retailer power
What if the retailer has the bargaining power?
Example: the Norwegian grocery industry.
Gabrielsen & Sørgard, “Discount Chains and Brand Policy”, Scandinavian
Journal of Economics 1999.
Johansen & Nilssen, “The Economics of Retailing Formats”, unpublished
2013.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 6
Vertical foreclosure
 A firm has control over the production of a product or
service that is an essential input for producers in a
potentially competitive industry. The competition in this
industry can be altered by the firm by denying or limiting
access to the input.
 Essential facility
- bottleneck
- network industries: firms need access to network to
deliver product or service
 telecom: AT&T, Telenor
 power: Statnett
 shipping: harbours
 railway: Eurotunnel
- outside network industries: firms are at a disadvantage
without access
 computer reservation systems for airlines
 cooperatives: ski lifts, newspapers, ATMs
 distribution of goods: retailing chains (food
stores, pharmacies, book stores, pubs)
 Horizontal foreclosure: bundling, tying
- complement products with one firm having (near)
monopoly in one of the markets
- Microsoft
 Windows/internet browser
 Windows/media player
Tore Nilssen – Strategic Competition – Theme 7 – Slide 7
The Chicago School
Upstream
monopolist
Downstream
subsidiary
Downstream
competitor
 There’s only one monopoly profit to be had.
 Vertical integration and vertical foreclosure cannot be
harmful.
 If there is a problem, it is that there is no competition
upstream.
The foreclosure doctrine
The upstream firm does indeed have incentives to favour
one downstream firm, such as a downstream subsidiary.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 8
A reconciliation: the role of commitment
 Having contracted with one downstream firm, the
upstream firm has incentives to contract further with
other downstream firms, even though these firms in turn
will compete with the first firm and decrease its profit.
 The first downstream firm realizes this and is less willing
to sign a contract. This reduces the upstream firm’s
profit.
 The upstream firm will be looking for ways to get around
this problem.  Vertical foreclosure
 Analogue: The durable-good monopolist. (Ronald
Coase)
Model
U
D1
D2
Consumers
p = P(q)
Tore Nilssen – Strategic Competition – Theme 7 – Slide 9
Timing
Stage 1: Firm U offers firms D1 and D2 tariffs T1() and
T2() for purchase of the intermediary good. Each Di then
orders a quantity qi and pays Ti(qi).
Stage 2: Firms D1 and D2 transform intermediate good into
final good and sell at price p = P(q1 + q2).
Define:
Qm = arg maxq {[P(q) – c)]q}
pm = P(Qm), m = (pm – c)Qm
Observable contracts
Firm U offers (qi, Ti) = (Qm/2, pmQm/2) to each downstream
firm. They both accept and sell in total monopoly quantity
at monopoly price. No rationale for foreclosure.
But can firm U commit to these contracts?
 If U and D2 agree on (q2, T2) = (Qm/2, pmQm/2), then
firms U and D1 would want to sign a contract that
maximizes their joint profit given the U/D2 contract, with
a quantity q1 given by:
q1 = arg maxq {[P(Qm/2 + q) – c)]q} > Qm/2.
 Anticipating this, firm D2 would turn down the (Qm/2,
pmQm/2) offer.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 10
Secret contracts
Passive beliefs: If a firm receives an unexpected offer, it
does not revise its beliefs about the offer made to its rival.
Consider a candidate equilibrium in which firm Dj is
offered a quantity qj. Whatever firm Di is offered, it still
believes that firm Dj is offered qj.
Firm U offers firm Di a quantity qi so that the joint profit
for U/Di is maximized, given the offer of qj to firm Dj:
qi = arg maxq {[P(q + qj) – c]q}
This is the same problem as the one facing a Cournot
duopolist.
q1 = q2 = qC – the Cournot quantity
The profit of the upstream firm:
U = 2C < m
 The upstream firm suffers from its inability to commit.
 The problem becomes more severe the larger the number
of downstream firms.
 The more competitive the downstream industry, the more
interested is the upstream bottleneck owner in
foreclosure in order to retain profit.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 11
Why does the upstream firm foreclose access?
Not in order to extend its market power to the downstream
market, but rather in order to re-establish the market power
lost because of its inability to commit.
Downward integration
Firm U buys one of the downstream firms. It credibly
offers the monopoly quantity Qm to its own affiliate and
nothing to the other.
Bypass: Sometimes, there is an alternative supplier
available to the non-integrated firm, so that the foreclosing
firm can be bypassed. Still, if the alternative supplier is less
efficient – for example, has higher production costs ĉ > c –
foreclosure with bypass is inefficient.
Exclusive dealing
 By entering an exclusive-dealing contract with D1, firm
U commits itself not to supply to D2.
 A substitute for vertical integration.
Tore Nilssen – Strategic Competition – Theme 7 – Slide 12
Auctions
Auction:
 One seller and a small number of potential buyers
The mirror image –
Contract auction / Procurement auction:
 One buyer and a small number of potential sellers.
 The buyer decides on the purchasing procedure,
potential sellers bid their prices.
When are auctions used?
 A unique object
- well defined? indivisible?
 Uncertainty about who should get the object / the
contract
 Uncertainty about the object’s value / the project costs
 Commitment to selling / buying procedure
Tore Nilssen – Strategic Competition – Theme 8 – Slide 1
Alternatives to auctions
Market
- decides who gets the object / project
- but how to determine the price?
Bargaining
- determines the price
- but how to determine who is the counterpart?
Handing out for free
- beauty contest
- lobbying costs
Two concerns with an auction
 For society - efficiency: Is the object bought by the
bidder with the highest willingness to pay?
 For the seller: Is the price the highest possible?
Several auction procedures
How are these questions affected by the procedure chosen?
Tore Nilssen – Strategic Competition – Theme 8 – Slide 2
Various kinds of auctions
 Sealed bids vs. open bids
 Open bids
- Ascending bids – English auction
 bidders submit higher and higher bids until
only one bidder remains
 art, collectibles
- Descending bids – Dutch auction
 seller starts with a high price and cries out
lower and lower prices until a bidder accepts
 flowers (Netherlands), fish (Israel), tobacco
(Canada)
 Sealed bids
- First price:
 The bidder with the highest bid wins and pays
his bid.
 real estate, government procurement
- Second price:
 The bidder with the highest bid wins and pays
an amount equal to the second highest bid.
 Vickrey auction [Vickrey, J Finance 1961]

- William Vickrey, Nobel laureate 1996
stamps etc. [Lucking-Reiley, J Econ Perspectives 2000]
Tore Nilssen – Strategic Competition – Theme 8 – Slide 3
Basic model
 Bidders are risk neutral
 Bidders’ valuations are different but independent
 Each bidder knows only his own valuation
 Seller doesn’t know any bidder’s valuation
 No observable differences among the bidders
 Reservation price?
Tore Nilssen – Strategic Competition – Theme 8 – Slide 4
Bidder behaviour
(i)
English auction
- continuing bidding is profitable as long as
own valuation > current high bid
- this strategy is independent of what other bidders do
(dominant strategy)
- the winner is the one with highest valuation
 efficiency
- price is (just above) second highest evaluation
Tore Nilssen – Strategic Competition – Theme 8 – Slide 5
(ii)
Sealed-bid second-price auction
bidder B’s valuation =
bidder B’s bid =
largest bid from others =
v
b
a
 With a valuation of v, what should be bidder B’s bid, b?
Distinguish between two cases:
a > v: B’s decision does not matter
a < v: B wins if b > a, and earns (v – a)
 Bidding b < v reduces B’s chances to win but does not
affect what he has to pay if he wins.
 Optimum bid: b = v
(dominant strategy)
 The winner is the one with highest valuation
 Efficiency
 The price equals second-highest valuation
 English auction and sealed-bid second-price auction are
equivalent with respect to winner and price.
 Contract auction:
- winner is the one with lowest cost
- price equals second-lowest cost
 Calculating the bid is easy
Tore Nilssen – Strategic Competition – Theme 8 – Slide 6
(iii)
Sealed-bid first-price auction
 Bidder trades off two concerns:
Bidding b < v
- reduces his chances to win; not good.
- reduces the price he has to pay if he wins; good.
 This trade-off makes the optimum bid lower than v.
 The bidder knows that other bidders think the same way:
All bidders bid below their valuation. This makes the
optimum bid even lower.
 This also holds for (iv) Dutch auction
 The winner is the one with the highest valuation
 The price equals highest bid, which is lower than highest
valuation
 Expected price = Expected second-highest valuation
 Calculating bid is difficult
Tore Nilssen – Strategic Competition – Theme 8 – Slide 7
Equilibrium bid – sealed-bid first-price auction
n bidders, vi  [vl, vh], i  {1, …, n}
cumulative distribution function: F(vi), i  {1, …, n}
Let’s focus on a symmetric equilibrium. Bidders are not
identical, since valuations differ. But there are no
observable differences, so their valuations are all drawn
from the same cdf.
In a symmetric equilibrium, there exists some function
B(v), which is the same for all players, so that if one’s
valuation is v, the equilibrium bid is B(v).
Consider bidder i. He does not know the other bidders’ vs
but believes that their bids depend on their valuations
according to the function B(v). Assume: B’ > 0.
 A bid of b implies a valuation equal to B-1(b).
The probability that i’s bid bi is the winning bid =
[F(B-1(bi))]n – 1
Bidder i’s expected profit:
i = [vi – bi][F(B-1(bi))]n – 1
Tore Nilssen – Strategic Competition – Theme 8 – Slide 8
Optimum bid satisfies:

 i
0
bi
d i  i  i dbi  i



 [F(B-1(bi))]n – 1
dvi vi bi dvi vi
In a symmetric equilibrium: bi = B(vi),  i.  vi = B-1(bi)
In equilibrium, bidders’ beliefs about each other’s
valuations are correct.

d i
n 1
 F vi 
dvi
Assume (reasonably): i = 0 if vi = vl.  B(vl) = vl.
Integration:
vi
 vi    F  x n 1 dx
vl
Two expressions for bidder i’s profit – must be equal.
i = [vi – bi][F(B (bi))]
-1
n–1
vi
=
n 1
 F  x  dx
vl
vi
 F  x  dx
 Bvi   bi  vi  v
l
n 1
F vi n 1
Tore Nilssen – Strategic Competition – Theme 8 – Slide 9
Common for all four kinds of auctions (in the base model):
 Efficiency: Object to the bidder with highest valuation
(or lowest cost)
 Revenue equivalence: All four kinds give the seller the
same expected income.
 An increase in the number of bidders increases the
expected price.
- the more bidders, the higher is the expected secondhighest valuation.
Difference among the auctions:
 Bid more difficult to calculate in sealed-bid first-price
and Dutch auctions than in sealed-bid second-price and
English auction.
Tore Nilssen – Strategic Competition – Theme 8 – Slide 10
Seller’s reservation price
Revenue equivalence in the basic model: Seller indifferent
between auction procedures. But what about a reservation
price?
A parallel situation: The monopolist’s problem
A monopolist trades off two concerns:
 wants to sell large quantities  low price
 wants to earn a profit per unit sold  high price
Optimum trade-off: Price above marginal cost
Auction: Seller trades off the same two concerns:
 wants to sell the object  low reservation price
 wants to earn a profit if the object is sold
 high reservation price
The two highest valuations: v1, v2
Reservation price: r
Three cases:
v1 > v2 > r: increasing r has no effect
(i)
(ii)
v1 > r > v2: increasing r increases the price
r > v1 > v2: increasing r reduces the chances to sell
(iii)
Tore Nilssen – Strategic Competition – Theme 8 – Slide 11
Optimum reservation price with 1 bidder
Bid = r or nothing
Seller’s own valuation: v0
Seller’s expected profit:
(r) = r[1 – F(r)] + v0F(r)
FOC:
[1 – F(r)] – rf(r) + v0f(r) = 0
1  F r 
 J r 
f r 
i.e., marginal cost = marginal revenue
 r = J-1(v0)
 v0  r 
Generally:
If highest bidder has valuation v, his expected gain is
1  F v 
f v 
so that the expected price in this case is
1  F v 
v
 J v 
f v 
The seller sells only if J(v)  v0 for the highest bid
 r = J-1(v0)
Effiency with a reservation price:
 With a reservation price, the object may not be sold,
even if a bidder exists with v > v0.
 Ex-ante efficiency vs. ex-post efficiency.
Tore Nilssen – Strategic Competition – Theme 8 – Slide 12
Some extensions
(i)
Observable differences among the bidders
Example:
Public procurement – domestic vs. foreign firms.
Suppose foreign firms are more cost effective than
domestic ones.
 English auction and sealed-bid second-price auction are
still efficient.
 Sealed-bid first-price auction no longer efficient: it is
possible to win the auction without having the lowest
cost.
 It is optimum for the procurer to discriminate between
bidder groups, and one is no longer certain that the
project is won by the lowest-cost bidder.
 In the example: It is optimum to discriminate in favour
of the domestic firms. This favouring
- increases the chance of getting an inefficient
supplier, but also
- lowers the bid from the efficient firms
Tore Nilssen – Strategic Competition – Theme 8 – Slide 13
(ii)
Risk-averse bidders
 In a sealed-bid first-price auction, risk-averse bidders bid
higher than risk-neutral ones. An increase in the bid
(1) increases the chance of winning, and therefore
getting something
(2) reduces what one earns in case of winning.
With risk aversion, (1) gets more important than (2)
 Contract auction: Risk averse bidders bid more
aggressively than risk neutral bidders.
 The seller gains more in a sealed-bid first-price auction
than in a sealed-bid second-price auction.
(iii)
Correlated valuations
 Extreme case: identical valuations. Bidders do not know
the object’s true value but have access to different pieces
of information about this value. No bidder knows what
other bidders know.
 More common in auctions than in contract auctions?
Auctions:
- buying for resale
- exclusive rights
Contract auction
- pioneering projects with great cost uncertainty
for all potential suppliers
Tore Nilssen – Strategic Competition – Theme 8 – Slide 14
 “Winner’s curse”
- Bidders base bids in a sealed-bid auction on
estimates. The bidder with the most optimistic
estimate wins.
- If you win, then you will wish to revise your
estimate: The winner is the most optimistic one.
- But this is taken into consideration in the bids: Bids
are even lower because of the “winner’s curse”.
 In an English auction, bidders learn from each other
during the bidding process. This reduces the winner’scurse problem.
- With correlated values, an English auction is
preferred by the seller to the other kinds.
 Asymmetric information
- one bidder knows the object’s true value
- US offshore oil and gas lease auctions
- Porter, Econometrica 1995
Tore Nilssen – Strategic Competition – Theme 8 – Slide 15
Other issues
 Collusion
- second-price auction better for sustaining collusion
among bidders than first-price auction
- open bids better than closed bids
- contract auctions: Norsk Standard
 divisible objects
- securities, quotas
 combined bids
- petroleum: price on exploration right + production
fee
- vague projects: price + content
 entry costs, number of bidders, participation fee
 auctioning incentive contracts
 competition for a market vs. competition in a market
Tore Nilssen – Strategic Competition – Theme 8 – Slide 16
Efficiency of auctions
 Which auction procedure to use?
- revenue equivalence
- easily calculated bids
 sealed-bid second-price auction
But: risk aversion? correlated values?
 Which objects are sold most effectively in an auction?
- unique object
- uncertainty about willingness to pay:
how large? who?
 Does price affect efficiency?
- one unit – no quantity effects from price change
- divisible objects (quotas, securities): quantity
effects
Repeated auctions
- Less aggressive bidding today in order not to reveal
one’s high valuation before future auctions
(the ”ratchet” effect)
- better to have large projects? negotiating renewal with
current supplier?
- Capacity constraints: The winner of a contract today
may not have capacity to participate in the next
round.
Tore Nilssen – Strategic Competition – Theme 8 – Slide 17
Mergers
Why merge?
 reduce competition – increase market power
 cost savings – economies of scale and scope
Why allow mergers?
 cost savings
o Oliver Williamson: the efficiency defense
Williamson’s point: It may not take a huge cost saving to
dominate the deadweight loss from a merger.
Tore Nilssen – Strategic Competition – Theme 9 – Slide 1
But note:
 What if the pre-merger price is not competitive?
o Larger cost savings needed to outweigh deadweight
loss.
 Production reshuffling: More of the production in the
industry will be made by the low-cost firm – an
additional source of cost savings in the industry.
 What is the appropriate welfare standard?
 consumer welfare standard
 total welfare standard
 What are the long-term effects of the merger?
 R&D, capacity investments, new products, etc.
Tore Nilssen – Strategic Competition – Theme 9 – Slide 2
Static effects of mergers
 Unilateral effects
 In general, welfare analyses of mergers are complex –
even within rather simple models.
 An alternative: a sufficient condition for a merger to be
welfare improving
 The Farrell-Shapiro criterion
A merger affects
 the merging firms
 price
 costs
 the non-merging firms
 price
 consumers
 price
When a merger is proposed, then – presumably – it is
profitable for the merging firms. So the competition authority
– when looking for a sufficient condition for a welfareimprovement – can limit the analysis to the merger’s effect on
(i)
(ii)
non-merging firms, and
consumers
 the external effect of a merger
Cost savings affect to a large extent only the merging parties.
So focusing on the external effect, we do not need to assess
vague statements about cost savings from a merger.
Tore Nilssen – Strategic Competition – Theme 9 – Slide 3
If the merger leads to a higher price, then non-merging firms
benefit, and consumers suffer. But what is the total external
effect?
A merger model with Cournot competition
X – total output in the industry
xi – firm i’s output
yi – all other firms’ output: yi= X – xi
Firm i’s costs: ci(xi)
Inverse demand: p(X)
Firm i’s first-order condition:

p(X) + xip’(X) – ci’(xi) = 0.
p(xi + yi) + xip’(xi + yi) – ci’(xi) = 0
Firm i’s response to a change in other firms’ output – total
differentiation wrt xi and yi:
"
"
2
"
From which we find firm i’s response to a change in total
output:
dxi = Ridyi  dxi(1 + Ri) = Ri(dxi + dyi) = RidX

1
"
"
′

0
Tore Nilssen – Strategic Competition – Theme 9 – Slide 4
Welfare effects of a merger
Two sets of firms:
I – insiders
O – outsiders
An infinitesimal merger
 dXI – a small exogenous change in industry output
Change in welfare from this merger:
′
∈






Changes in output assessed at market price p.
cI – insiders’ total costs
Note: dxi = – idXI for each outsider firm
From an outsider firm’s FOC: p – ci’ = – xip’(X)
The external effect of the merger: dE = dW – dI.
The market share of a firm: si = xi/X.


′
∈
′

∈

∈

∈
Tore Nilssen – Strategic Competition – Theme 9 – Slide 5
Here, p’ < 0 and, typically, dXI < 0.
So the external effect of a merger (the accumulation of many
infinitesimal mergers) is positive if and only if:
 s
iO
i i
 sI
!
 An upper bound on the merging firms’ joint (pre-merger)
market share in order for their merger to improve welfare.
Examples
1. A simple model: constant marginal costs, linear demand
ci” = 0, p” = 0  i = 1.
Before merger: all firms of equal size. The external effect is
positive if the set of merging firms is less than half of all
firms:
sI   si  m < n/2
iO
 But: will such a merger always be profitable?
Tore Nilssen – Strategic Competition – Theme 9 – Slide 6
2. A more sophisticated model: merger between “units of
capital”.
The Perry-Porter model.
Cost function: C(xi, ki) =
. Marginal costs:
Interpretation: k is an input factor that is in total fixed supply
within the industry and not available outside the industry (such
as “industry knowledge”). The only way for a firm to expand
is to acquire k from other firms, such as through a merger. The
more k a firm has, the lower are its costs – cost savings from
mergers.
A merger between two firms with k1 and k2 units of capital
creates a firm with k1 + k2 units of capital.
Also assume linear inverse demand: P(X) = a – X.

i 
ki
c  ki
FOC for firm i:
p + xip’ – C’(xi) = 0  p  xi 
i 
c
x
xi  0  p  i 
ki
i
xi si

p 
(since  = – D’p/D = p/X when demand is linear)
Tore Nilssen – Strategic Competition – Theme 9 – Slide 7
The external effect is positive if:
sI 
1
s


iO
2
i
 The size of the external effect depends on how
concentrated the non-merging part of the industry is!
 A merger is more likely to be welfare-enhancing if the
rest of the industry is concentrated.
 A merger among small firms leads to the other, big, firms
expanding, which is good. (Production reshuffling)
Criticism of the Farrell-Shapiro approach
 The presumption that the merger is privately profitable
may not be valid
 Empire building
 Tax motivated mergers
 Pre-emption (or encouragement) of other
mergers
Coordinated effects of a merger
 A merger’s effect on collusion
 What effect does a merger have in an industry where
firms collude? – On balance: unclear.
 The merging firms now earn more and have
reduced incentives to cheat on the collusive
agreement after the merger.
 The non-merging firms now earn more without
collusion and therefore have increased
incentives for breaking out of the collusive
agreement after the merger.
Tore Nilssen – Strategic Competition – Theme 9 – Slide 8