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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 R1s2 , 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 in1 q i i(q1, …, qn) = qiP(Q) – Ci(qi) i dQ PQ 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 na 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)] 41 1 p1 2 p 2 41 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 ½sm + V sm 2V 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: 2m 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 + … ] 2m 1 1 1 1 2 21 21 2 42 + – 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 p1p2 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 ba 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 ba a 2 2t 1 a b 2 2 31 a b 3 5a b 1 0, if a 61 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 a2 3a b 1 0 a p2 a 61 a b 31 a b 61 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. pc 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 a1 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 11 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 * 2s c t 3 2s 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 sc 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 K1K 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 x1x2 2 2 x1x2 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 d2/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 d2/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 p1p2 p2 p1p2 First term positive 2 D1 Slope of the best response positive unless very p1p2 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 p1c1 p12 dp1 2 1 p1c1 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 p1c1 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 ii 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: maxa 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 D1 F D1 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 Dc 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 Dc 1 cc Dc 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 3c 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 = 2C < 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 Bvi 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 – dI. 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 iO 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 iO 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 iO 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