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INDUSTRIAL ECONOMICS II
Prof. Davide Vannoni
Handout 4
Entry, accomodation and exit
1.
Informal introduction
2.
The Bain-Sylos Labini- Modigliani model of limit pricing
3.
A general framework (Fudenberg and Tirole, 1984, AER)
4.
Deterrence of entry
5.
Accomodation of entry
6.
Strategic complements or strategic substitutes?
Useful paper: Vives X. (2005) “Games with strategic complementarities:
new applications to industrial organization”, International Journal of
Industrial Organization, pp. 625-637.
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1.
Informal introduction
Industries with positive profits should attract new firms (entrants). How
should established firms (incumbents) react in the face of an entry threat?
Three kinds of strategic behaviour:
Blockaded entry: incumbents compete as if there were non threat of entry.
Even so, the market is not attractive enough to entrants (in this case the
strategic analysis is uninteresting).
Deterred entry: Entry is not blockaded but incumbents find it profitable to
modify their behaviour to successfully deter entry.
Accomodated entry: Entry is not blockaded and incumbents find it more
profitable to let entrants enter than to erect costly barriers to entry.
Relevance for competition policy
 Limit pricing: potential entry plays a key role in the checklist of
any antitrust authority (merger cases, assessment of abuse of
market power, vertical restraints etc.) Therefore, we need to know
whether incumbent firms can neutralise/deter such entry by
pricing ‘low’ (e.g. by exploiting asymmetric information), in order
to avoid subsequent competition
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 Predatory behaviour is illegal under most jurisdictions, but very
difficult to prove. Is it credible? And under what circumstances?
Development of ideas in the academic IO literature
 Structure-conduct-performance (Harvard), in a rare piece of
formal theory, developed the Bain/Sylos-Labini/Modigliani model
of limit pricing. It showed how barriers to entry were a necessary
condition for the abuse of market power. Similarly, the belief that
predatory pricing can/does take place was one of the pillars of its
belief in active antitrust intervention as essential to the functioning
of a competitive economy.
 Chicago school contested both concepts – argued that neither
strategy was credible, and therefore never existed
 Game-theoretic revolution – initially seemed to side with Chicago
by showing how both strategies were logically flawed (backward
induction). However, important papers (e.g. Kreps & Wilson,
Milgrom & Roberts subsequently showed how they can be
credible and are therefore logical possibilities.
Asymmetric
information plays an important part in the story.
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2. The Bain/Sylos-Labini/Modigliani Model of Limit Pricing
Definition and intuition
Bain (1949, p.449):
“established sellers persistently ..forgo prices high enough to
maximise industry profit for fear of thereby attracting new
entry to the industry and thus reducing the demands for their
outputs and their own profits”
In the Bain/Sylos-Labini/Modigliani homogeneous product model, the
incumbent monopolist supplies the limit output (corresponding to the limit
price). This is the minimum output required to make the profits of an
entrant non-positive. This is coupled with the Sylos postulate, which
refers to the entrant’s expectations of the incumbent’s behaviour postentry. Specifically, the entrant is supposed to believe that the incumbent
will produce the same amount after entry as before. Thus, by setting the
limit output, the incumbent convinces the entrant that there is no chance of
making profits post-entry.
Figure 1
P
PL
Pe
De
D
c
Qe QL
Q
4
Formally:
1
Entrant does not enter if he is not making profits
2
2. Under the Sylos Postulate, the incumbent can deter such entry
by supplying QL before entry. He can therefore charge PL.
3.
While this may be less than the monopoly price, so long as it exceeds
duopoly price, he will wish to limit price.
So why is this a problem? After all, it means that the incumbent doesn’t
charge full monopoly price. Answer: although the limit (entry deterring)
price might not be as high as full monopoly price, it’s still higher than
what it would be (duopoly price?) if entry were to occur.
The conventional critique
The problem is that the Sylos postulate is a noncredible threat: an
incumbent would typically find it profit maximising to accommodate entry
by reducing its output – once the entrant is in, there is no point in the
incumbent continuing to supply a large output since this harms his own
profits. At this point, he will want to retreat to duopoly output. The
entrant knows this in the first place, so he is not deterred.
Entrant
Incumbent
Accommodate
Fight
In
d, d
w, w
Out
m, 0
m, 0
where m > d > w d = duopoly, w = war with w<0
Two Nash equilibria, but only one (duopoly profits) is subgame perfect
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Figure 2
stay out
(0, m)
(d, d)
Entrant
accommodate
enter
Incumbent
(w w )
fight
The contribution of Game Theory
Entry deterrence may be feasible given the ability to pre-commit
(investment in some sort of capacity) to a tough response to entry. See
Fudenberg and Tirole later on in this lecture. But beyond this, there is a
literature on the strategic use of price alone.
A classic paper of this sort is: Milgrom-Roberts: limit pricing under
asymmetric information (Tirole pp368-74)
This is a classic two-period game which shows how limit pricing can,
indeed, be a rational strategy. It all hinges on asymmetric information on
costs.
a brief summary
 entrant does not know, before entry, whether incumbent has costs
which are ‘low’ or ‘high’
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 If its costs are ‘low’, then entry would not be profitable, i.e. the
duopoly profits of the entrant when competing with a low cost
competitor would be negative
 Ideally, incumbent wants to signal to entrant that he is low cost. But
how can he do this?
By charging a low price initially?
Not
necessarily, because the entrant may believe that the incumbent is
‘bluffing’.
 Nevertheless, it turns out that this can sometimes be possible. It all
depends on the parameters of costs and demands.
They show how limit pricing might occur in one of two ways:
 separating equilibrium. This occurs where it is realised by both
incumbent and potential entrant that the optimal first period price for
a low cost incumbent is different from that of a high cost incumbent.
For a high cost incumbent, that price is its unconstrained monopoly
price, accepting, that entry will occur in the second period. But for
the low cost incumbent, it is a limit price (i.e. less than unconstrained
monopoly price.) Here, the incumbent has to signal to the entrant
that it is, indeed, a low cost firm. The circumstances where this
occurs are shown in figure 9.2 in Tirole.
 pooling equilibrium. This occurs when it is optimal for a high cost
incumbent to set the same price as a low cost incumbent. That price
is the unconstrained low-cost monopoly price. In this case, it is a
high cost incumbent who is limit pricing.
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Symmetric
Information
Incumbent type:
High cost
Low cost
Entry
No Entry
Welfare
Asymmetric Information
Separating
equilibrium
Entry
No entry, limit
prices
Pooling equilibrium
higher in period 1
higher in 1, lower in 2
No entry, limit prices
No entry
So how does limit pricing affect welfare? If it is practised by a low cost
incumbent (because a separating equilibrium) it is beneficial to consumers,
because he has to set a lower price than under symmetric information. If it
is practised by a high cost incumbent (pooling equilibrium), it is beneficial
to consumers in period 1, but harmful in period 2 (because the low cost
entrant has not entered).
Which actually occurs depends on the demand and cost conditions
3.
A general framework
Modelling strategy:
Incumbents have a first mover advantage. This temporal asymmetry
models the obvious fact that incumbents are already in the market whereas
entrants are not.
Incumbents may exploit their first mover advantage by making a sunk
investment, that is an investment which produces a stream of profits in
future periods but that cannot be resold (no second-hand market). From a
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strategic point of view, the important aspect of a sunk investment is that it
can be thought as a credible commitment.
First stage: firm 1 (the incumbent) chooses the size of a sunk investment,
K1 . It can be interpreted as a generic investment in production capacity, in
R&D, in advertising, in the training of personnel, in the creation of a sales
force, etc.
Second stage: firm 2 (the entrant) observes K1 and decides whether to
enter or not.
Non-entry
If firm 2 decides not to enter, it makes zero profits, whereas firm 1 enjoys
a monopoly position in the second stage, and its profits are equal to
 1m ( K1 , x1m ( K1 ))
where x1m ( K1 ) is the monopoly choice in the second period (e.g. price or
quantity) as a function of K1.
Entry
If firm 2 decides to enter, the two firms choose x1 and x2 simultaneously
and non-cooperatively. Their profits are therefore:
 1 ( K1 , x1 ( K1 ), x2 ( K1 ))
 2 ( K1 , x1 ( K1 ), x2 ( K1 ))
If we take the choice in the first stage as given, the post entry choices x1
and x2 are determined by the Nash equilibrium (supposing it exists, it is
unique and stable),
( x1* ( K1 ), x2* ( K1 ))
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What we are mainly interested in is to assess the effect of changes in K1 on
profits. The total derivative of  1 with respect to K1 can be written as
d 1  1  1 dx2*  1 dx1*



dK1 K1 x2 dK1 x1 dK1
This expression makes it clear than when K1 changes there are three
effects. Firstly, the change in K1 directly affects  1 (direct effect).
Secondly, the change in K1 affects firm 2’s optimal choice, x2* which in
turn affects  1 (strategic effect). Thirdly, the change in K1 affects firm 1’s
optimal choice, x1* which in turn affects  1 . However, since x1 is chosen
optimally , a small change in x1 has a zero effect on  1 .
Analogously, the total derivative of  2 with respect to K1 can be written
as:
d 2  2  2 dx1*  2 dx2*



dK1 K1 x1 dK1 x2 dK1
As before,
the change in K1 may directly affect  2 (direct effect).
Secondly, the change in K1 affects firm 1’s optimal choice, x1* which in
turn affects  2 (strategic effect). Thirdly, the change in K1 affects firm 2’s
optimal choice, x2* which in turn affects  2 . However, since x2 is chosen
optimally , a small change in x2 has a zero effect on  2 .
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4.
Deterrence of entry
In order to deter entry (the case where entry is blockaded is ruled out) the
incumbent chooses a level of K1 in the first stage so that
 2 ( K1 , x1* ( K1 ), x2* ( K1 )) =0
Should firm 1 make a big investment in the first stage or should firm 1
make a small investment? Obviously the answer has to be found by
looking at the total derivative  2 with respect to K1
d 2  2  2 dx1*


dK1 K1 x1 dK1
In most economic applications, the direct effect is likely to be negligible.
Most of the effect is channelled though the strategic effect.
The investment makes firm 1 tough if
 2 dx1*
0
x1 dK1
or soft if
 2 dx1*
0
x1 dK1
Implication: in order to deter entry firm 1 should overinvest only if this
makes firm 1 tough. If on the contrary a big investment makes firm 1 soft,
then firm 1should underinvest.
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5. Accomodation of entry
Let us suppose that entry deterrence is too costly and therefore firm 1
decides to accomodate firm 2. In this case the incentive to invest depends
on the effect of the first stage investment on firm 1’s second stage profits.
d 1  1  1 dx2*


dK1 K1 x2 dK1
Even if the direct (cost minimisation) effect is unlikely to be zero (or even
negligible), we will ignore it and concentrate instead on the sign of the
strategic effect:
 1 dx2*  1 dx1* dx2*  1 dx1* ' *


R2 ( x1 )
x2 dK1 x2 dK1 dx1 x2 dK1
Let us assume that
 1
 2
sign(
)  sign(
)
x2
x1
it follows that
 1 dx2*
 2 dx1*
sign(
)  sign(
) sign( R2' ( x1* ))
x2 dK1
x1 dK1
The sign of the strategic effect can be related to investment making firm 1
tough or soft (as in the deterrence of entry case) and to the slope of the
second stage best response (or reaction) function.
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The taxonomy of business strategies (almost an animal farm)
Top dog
If a big investment makes firm 1 tough and the best response function is
downward sloping
 2 dx1*
(
)0
x1 dK1
( R2' ( x1* ))  0
firm 1 should play the “top dog” strategy, that is it should be big to look
tough and therefore induce a soft response.
Lean and hungry look
If a big investment makes firm 1 soft and the best response function is
downward sloping
 2 dx1*
(
)0
x1 dK1
( R2' ( x1* ))  0
firm 1 should stay lean and hungry, that is should be small to look tough
and therefore induce a weak response.
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Fat cat
If a big investment makes firm 1 soft and the best response function is
upward sloping
 2 dx1*
(
)0
x1 dK1
( R2' ( x1* ))  0
firm 1 should play the “fat cat” strategy, that is it should be big to look soft
and therefore induce a soft response.
Puppy dog
Finally, if a big investment makes firm 1 tough and the best response
function is upward sloping
 2 dx1*
(
)0
x1 dK1
( R2' ( x1* ))  0
firm 1 should play the “puppy dog” strategy, that is should be small to
look soft and therefore induce a soft response.
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6. Strategic substitutes or strategic complements?
Price and quantities are usually characterised as strategic complements
( Ri' ( p j )  0) and strategic substitutes ( Ri' (q j )  0) respectively. However
this is not a general law since it crucially depends on the sign of the cross
partial derivative:
sign( Ri' ( x j ))  sign( iij ( Ri ( x j ), x j ))
Counter example 1 (quantity competition)
 i (qi , q j )  qi P(qi  q j )  Ci (qi )
 iij (qi , q j )  P'qi P' '
P ' is negative. A sufficient condition for the strategic-substitute property is
P' '  0 (linear inverse demand function) or P' '  0 (strictly concave inverse
demand function). However the property may fail for sufficiently convex
inverse demand functions.
Counter example 2 (price competition with differentiated products)
i ( pi , p j )  pi Di ( pi , p j )  Ci ( Di ( pi , p j ))
Di
 2 Di
D Di
'
 ij ( pi , p j ) 
 ( pi  Ci )
 Ci'' i
p j
pi p j
pi p j
i
To simplify, assume that both the cost and the demand functions are linear
Ci'  ci
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qi  a  bpi  dp j
where b is negative and d may be either positive (if the two goods are
demand substitutes) or negative (if the two goods are demand
complements).
It is easy to show that if goods are demand substitutes prices are strategic
complements, whereas if goods are demand complements prices are
strategic substitutes. In fact
 iij ( pi , p j )  d
Some applications of the taxonomy
Entry deterrence
Investment makes the incumbent
Aggressive
Optimal Strategy TOP DOG
Accomodating
LEAN/HUNGRY LOOK
Accomodation of the rival
Investment makes the incumbent
Strategic
Aggressive
Accomodating
TOP DOG
LEAN/HUNGRY LOOK
PUPPY DOG
FAT CAT
Substitutes
Strategic
Complements
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Example 1. Voluntary limitation of capacity
In a two stage model in which firm choose the productive capacity in the
first stage and then compete in prices in the second stage the optimal
strategy is to accumulate a low level of capacity in order to be less
aggressive in the second stage: PUPPY DOG
Example 2. Product differentiation
Linear city model in two stages. By locating at the extreme positions of the
segment line (0 and 1), firms avoid aggressive price competition in the
second stage: PUPPY DOG
Example 3. Investment on capacity
Two stage game in which incumbent in the first stage invests in capacity
bearing some sunk costs (no recoverability).
In the second stage incumbent and entrant compete by choosing quantities,
but the entrant must bear both costs of production and costs of installing
capacity, while the incumbent incurs only in costs of production, since
costs of installing new capacity appear only if it chooses to produce more
than the installed capacity.
Marginal costs of production: c
Marginal costs per unit of capacity: k
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Q2
RI
R’I
C
Q2
M
K=Q1
RE
Q1
C: Cournot Outcome; M: Maximum amount of quantity that the
incumbent can produce by investing in capacity in the first stage; RI =
Incumbent’s reaction function with marginal costs equal to c; RI’ and RE =
Incumbent’s reaction function and entrant’s reaction function with
marginal costs equal to c+k.
By investing in capacity in the first stage, the incumbent can ‘move’ the
equilibrium from C to M (in the case depicted in the figure from C to the
point in which K=Q1): TOP DOG
Example 4. Advertising
Stage 1: The incumbent firm contacts a portion of the consumers with an
advertising message. The consumers that buy the product are ‘captured’ by
the incumbent in the second stage (goodwill in terms of customers’fidelity)
Stage 2: The incumbent and the entrant compete for the remaining
consumers in a price competition setting. Note that by reducing the price
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in the second stage the incumbent must reduce the price also for the
‘captive’consumers (no price discrimination)
If the incumbent wants to accomodate entry: FAT CAT
If the incumbent wants to deter entry: LEAN AND HUNGRY LOOK
Example 5. Import Quotas and Export Subsidies
Import quotas: with an import quota foreign firms become PUPPY DOG,
in the case of strategic complements. If the quota is sufficiently high, such
strategy can be beneficial for both foreign and domestic firms (and
harmful for welfare), since it reduces price competition.
Export subsidies: with and export subsidy exporting firms are pushed to
act aggressively. In the case of strategic substitutes, the subsidy increases
profits and the market share of exporting firms: TOP DOG.
Example 6. Most favoured customer clause
It ensures the consumers of a product to be reimbursed of the difference
between the current price and the future price if the firms decide to lower it
in the future.
First stage: price competition; Second stage: price competition
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P2
P2*
E
P1*
P1
Equilibrium without the most favoured customer clause : E
P2
P2’
P2*
E’
E
P1* P1’
P1
Equilibrium with the most favoured customer clause (even unilateral!): E’
in both periods: FAT CAT
With the clause, if in the second period there is a price decrease (from P1’
to P1*), profits decrease by (P1’-P1*) per each unit sold in the first period.
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Example 7. Strategic manipulation of an installed base of customers
Period 1: There is only the incumbent that sells to customers a
good/service characterised by the presence of switching costs (the
customer must bear some costs in order to learn to use the product)
Period 2: The entrant and the incumbent play a Cournot game.
The incumbent’s reaction function is shifted upwards for existing
customers (since they demand the good without computing the switching
costs). By investing on an installed base in the first period, it is possible to
increase the market share in the second stage: TOP DOG
Q2
REXIST
RNEW
C
Q2
M
Size of installed base
RE
Q1
C: Cournot Outcome; M: Maximum amount of quantity that the
incumbent can produce by investing in installed base in the first stage.
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Example 8. Tying
One firm sells in two markets, A (monopoly) and B (price competition
with an entrant). By bundling the products A and B together (that is by
offering A and B together in a single package at a single price) it is
possible to foreclose the rival (or to deter entry).
The bundling decision has the effect of shifting in market B the reaction
function of the tying firm to the left: if the tying firm sells one further
bundle she gains profits in the monopolistic market A and can bear less
profits in market B. Of course if the entrant is not foreclosed (deterred) it
is not a good strategy.
Entry deterrence: TOP DOG (i.e. tying)
Accomodation: PUPPY DOG (no tying)
P2
E
P2
D
P1
P1
P2 = entry deterring price (limit price)
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