1. OT2012 1 Corporate Social Responsibility or Asymmetry of Payoff ?: An Investigation of Endogenous Timing Game joint work with Akira Ogawa

2. 2012/3/4 2 Our works related to this paper (1) Payoff Dominance and Risk Dominance in the Observable Delay Game: A Note (JoE 2009, joint work with Akira Ogawa). (2) On the Robustness of Private Leadership in Mixed Duopoly (AEP 2010, with Akira Ogawa) (3) Randomized Strategy Equilibrium and Simultaneous-Move Outcome in the Action Commitment Game with Small Cost of Leading (ORL 2011, with Takeshi Murooka and Akira Ogawa). (4) Price leadership in a homogeneous product market (JoE 2011, with Daisuke Hirata)

3. OT2012 3 price leadership The leader announces the price change first, and then other firms follow this price change. Some researchers suspect that this is a collusive pricing, implicit cartel. However, if we regard this as a price version Stackelberg, it is natural that a higher price of the leader induces a higher price of the follower (strategic complements)

4. OT2012 4 price leadership (Ono, 1978) Homogeneous product market, no supply obligation, duopoly, increasing marginal cost, price-setting. One firm chooses the price and then the other firm chooses its price after observing the price of the rival. (Stackelberg) He compares the equilibrium payoffs when the firm with higher cost is the leader to those when the firm with lower cost is the leader.

5. OT2012 5 Asymmetric Costs Y the MC of the lower cost firm 0 MC the MC of the higher cost firm

6. OT2012 6 Follower's pricing (1) Suppose that the leader's price is higher than the monopoly price of the follower. Then, the follower names its monopoly price and obtains the whole market. (2) Suppose that the leader's price is lower than the monopoly price of the follower. Then, (a) names a higher price than the leader and obtains the residual demand, or (b) the follower names the price slightly lower than the rival's and obtains the whole market. (price under- cutting)

7. OT2012 7 Firm 1's pricing Ono (1978) assume that the follower undercuts the leader's price. Predicting this behavior of the follower, the leader chooses its price.

8. OT2012 8 Residual demand Y D 0 MC P Follower's MC P1P1 Y2Y2 residual demand of the leader

9. OT2012 9 residual demand Y D 0 MC P Follower's MC residual demand of the leader

10. OT2012 10 Residual Demand Y D 0 MC P Follower's MC residual demand of the leader

11. OT2012 11 price leadership Suppose that the firm with lower cost becomes the follower.→It produces a lot as a price taker →Predicting this aggressive behavior, the firm with higher cost names a low price. Suppose that the firms with higher cost becomes the follower.→It does not produces a lot as a price taker →Predicting this less aggressive behavior, the firm with higher cost names a high price. ~ beneficial for both firms. He concludes that the lower cost firm takes price leadership if the cost difference between two firms is large.

12. OT2012 12 Contribution of Ono (1978) (1) pioneering work on Timing Game (2) pioneering work on Price Leadership ～ the lower cost firm becomes the leader (3) Mutually beneficial price leadership can appear when the cost difference between two firms are sufficiently large.

13. OT2012 13 Subsequent Works ・ Ono (1982) Oligopoly Version ・ Denekere and Kovenock (1992) ~Capacity Constraint →The firm with more capacity becomes the leader. ・ Amir and Stepanova (2006) ～ differentiated product market →The firm with lower cost firm becomes the leader and it is mutually beneficial if cost difference is large. ・ Ishibashi (2007) ~Capacity Constraint ＋ repeated game →The firm with more capacity becomes the leader.

14. OT2012 14 Problems in Ono(1978) (1) Is mutually beneficial leadership is always realized in equilibrium ？ ・ He did not formulate the Timing Game. (a) Is the outcome where the lower cost firm becomes the leader always an equilibrium ？ (b) Is it a unique equilibrium? (c) If not, the equilibrium with lower cost firm's leadership is robust ？ ~No game theoretic foundation

15. OT2012 15 Problems in Ono(1978) (2) Is price undercutting is always best reply? The answer is NO. undercutting is not always best reply.

16. OT2012 16 Dastidar (2004) Consider a Stackelberg duopoly with common increasing marginal cost in a homogeneous product market. Firm 1 names the price and after observing the price firm names the price.

17. OT2012 17 price-undercuttin price-undercutting Y D 0 P MC Firm 2's MC P1P1 Y2Y2

18. OT2012 18 no price-undercutting Y D 0 P MC Firm 2's MC P1P1 Y1Y1 Residual Demand P2P2

19. OT2012 19 price-undercutting vs non- undercutting A decrease in the price of the leader makes the undercutting strategy more profitable and non- undercutting strategy less profitable. →There exists p* such that the follower takes non- undercutting strategy if and only if p ≦ p*. In equilibrium, firm 1 names P 1 = p*, firm 2 takes non- undercutting strategy, and two firms obtain the same profits. Two prices appear in the homogeneous product market. The leader engages in marginal cost-pricing, while the follower is not.

20. OT2012 20 Problems in Ono(1978) (3) The assumption of price-undercutting is innocuous? The answer is NO. This assumption changes the results In equilibrium, the follower does not undercut the price. (i) The price leadership by the higher price firm is mutually beneficial even when the cost difference is small. (ii) It is a unique equilibrium, or it is the risk-dominant equilibrium.

21. OT2012 21 Hirata and Matsumura (2011) (i) The price leadership by the higher price firm is mutually beneficial even when the cost difference is small. (ii) It is a unique equilibrium, or it is the risk-dominant equilibrium.

22. OT2012 22 price-undercuttin price-undercutting Y D 0 P MC Firm 2's MC P1P1 Y2Y2

23. OT2012 23 no price-undercutting Y D 0 P MC Firm 2's MC P1P1 Y1Y1 Residual Demand P2P2 Firm 1's MC

24. OT2012 24 Intuition behind the results Suppose that the leader has a higher cost. ～ It is easy to induce the follower to take non-undercutting strategy (taking a residual demand). It can name the relatively higher price, and it is mutually beneficial.

25. OT2012 25 Stackelberg or Cournot Cournot (Bertrand) model and Stackelberg model yield different results. Simultaneous move model and sequential move model yield different results. Which model should we use? Which model is more realistic? An incumbent and a new entrant competes →sequential-move model There is no such asymmetry between firms →simultaneous-move model However, in reality, firms can choose both how much they produce and when they produce.

26. OT2012 26 Timing Games Firms can choose when to produce. Formulating a model where Cournot outcome and Stackelberg outcome can appear, and investigating whether Cournot or Stackelberg appear in equilibrium.

27. OT2012 27 Stackelberg Duopoly Firm 1 and firm 2 compete in a homogeneous product market. Firm 1 chooses its output Y 1 ∈ [0, ∞). After observing Y 1, firm 2 chooses its output Y 2 ∈ [0, ∞). Each firm maximizes its own profit Π i. Π i ＝ P(Y)Y i ー C i (Y i ), P: Inverse demand function, Y: Total output, Y i : Firm i's output, C i : Firm i's cost function I assume that P'+P''Y 1 <0 (strategic substitutes) ⇒ First-Mover Advantage

28. OT2012 28 Stackelberg's discussion on the market instability In the real world, it is not predetermined which firm becomes the leader. Because of the first-mover advantage, both firms want to be the leaders. Straggle for becoming the leader make the market instable. ～ This is just the idea for endogenous timing game. But he himself did not present a model formally. Some papers discussing this problem appeared at the end of 70s.

29. OT2012 29 Four representative timing games (1) Observable delay game (2) Action commitment game (3) Infinitely earlier period model (4) Seal or disclose (5) Two production period model

30. OT2012 30 Observable Delay Game Duopoly First stage: Two firm choose period 1 or period 2. Second Stage: After observing the timing, the firm choosing period 1 chooses its action. Third Stage: After observing the actions taking at the second stage, the firm choosing period 2 chooses its action. Payoff depends only on its action (not period).

31. OT2012 31 Possible Outcomes Both firms choose period 1 ⇒Cournot Both firms choose period 2 ⇒Cournot Only firm 1 chooses period 1 ⇒Stackelberg Only firm 2 chooses period 1 ⇒Stackelberg

32. OT2012 32 Equilibrium in Observable Delay Game Strategic Substitutes ⇒Both firms choose period 1 (Cournot) since Leader ≫ Cournot ≫ Follower Strategic Complements ⇒Only firm1 chooses period 1 (Stackelberg) or Only firm2 chooses period 1 (Stackelberg) since Leader ≫ Cournot and Follower ≫ Cournot.

33. OT2012 33 Asymmetric Cases It is possible that two firms have different payoff ranking. e.g., Price Leadership Firm 1 Leader ≫ Follower >> Bertrand Firm 2 Follower >> Leader >> Bertrand It is quite natural to think that firm 1 becomes a leader in equilibrium. cf Ono (1978,1982) Is it true?

34. OT2012 34 Matsumura and Ogawa (2009) Assumption U i L ≧ U i C Result If U 1 L ＞ U 1 F and U 2 F ＞ U 2 L, (i) firm 1's leadership is the unique equilibrium outcome, (ii) equilibrium outcomes other than firm 1's leadership is supported by weakly dominated strategies, or (iii) firm 1's leadership is risk dominant ⇒ Pareto dominance implies risk dominance in the observable delay game. ～ foundation for Ono's discussion.

35. OT2012 35 Pareto efficient outcome can fail to be an equilibrium in general contexts ＣＤ Ｃ（ 3,3 ）（ 0,4) Ｄ（ 4,0 ）（ 1,1 ） １ ２ Pareto Dominance →(C,C) Risk Dominance →(D,D)

36. OT2012 36 Pareto dominant equilibrium can fail to be the risk dominant equilibrium in general contexts CD C(3,3)(-100,-1) D(-1,-100)(1,1) １ ２ Pareto Dominance →(C,C) Risk Dominance →(D,D)

37. OT2012 37 risk dominance CD C(3,3)(-100,-1) D(-1,-100)(1,1) １ ２ Consider a mixed strategy equilibrium. Suppose that in the mixed strategy equilibrium each firm independently chooses C with probability q. Then (C,C) is risk dominant if and only if q <1/2.

38. OT2012 38 Observable Delay 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ C ≧ A, c ≧ a.

39. OT2012 39 Asymmetric Cases It is possible that two firms have different payoff ranking. e.g., Mixed Duopoly

40. OT2012 40 Pal (1998):mixed duopoly, domestic private firm, quantity-competition 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ (private firm) B>C>A, c>a, b>a Question: Derive the equilibrium outcome.

41. OT2012 41 Matsumura(2003): mixed duopoly, foreign private firm, quantity- competition 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ C>A>B, c>a, b>a Question: Derive the equilibrium outcome.

42. OT2012 42 Observable Delay, Matsumura (2003) 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ C>A>B, c>a, b>a

43. OT2012 43 Barcena-Ruiz (2007) :mixed duopoly, domestic private firm, price- competition 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ B>A>C, c>a>b Question: Derive the equilibrium outcome.

44. OT2012 44 Barcena-Ruiz (2007) 12 1(A,a)(C,b) 2(B,c)(A,a) １ ２ B>A>C, c>a>b

45. OT2012 45 Mixed Duopoly Mixed duopoly Quantity-competition→Stackelberg Price-Competition→Bertrand Private duopoly Quantity-competition→Cournot Price-Competition→Stackelberg Does asymmetry in objectives or welfare-maximizing objective yield contrasting results in mixed duopoly?

46. OT2012 46 Social responsibility approach Ghosh and Mitra (2010) Payoff θΠ＋(1-θ)W The same payoff of partially privatized firm Difference ~ Both firm has the same payoff (no asymmetry)

47. OT2012 47 Social responsibility approach Quantity-competition→Cournot Price-competition→Stackelberg Asymmetry in objectives, not welfare-maximizing objective, yields contrasting results in mixed duopoly.

48. OT2012 48 Endogenous Choice of Price- Quantity Contract Firms choose whether to adopt price contract or quantity contract, and then choose the prices or quantities. Singh and Vives (1984) showed that choosing the quantity (price) contract is a dominant strategy for each firm if the goods are substitutes (complements). Intuition (substitutable goods case) ： Choosing a price contract increases the demand elasticity of the rival, resulting in a more aggressive action of the rival.

49. OT2012 49 Endogenous Choice of Price- Quantity Contract in Mixed Duopoly For the private firm, choosing a price contract increases the demand elasticity of the rival, resulting in a less aggressive action of the rival (substitutable goods case). Thus, the private firm has an incentive to choose the price contract, as opposed to the private duopoly. For the public firm, choosing a price contract increases the demand elasticity of the rival, resulting in a more aggressive action of the rival. Thus, the public firm has an incentive to choose the price contract. →Bertrand competition appears in Mixed Duopoly (Matsumura and Ogawa, 2012)

50. OT2012 50 Social responsibility approach Quantity contract is chosen. Asymmetry in objectives, not welfare-maximizing objective, yields contrasting results in mixed duopoly.