1. OT2010 1 Relative Performance and R&D Competition Joint work with Susumu Cato ( 加藤晋 ) and Noriaki Matsushima ( 松島法明 )

2. OT2010 2 Plan of the Presentation (1) Relative Performance and Competitiveness of the market (2) Stability of Collusion (3) Relative Performance and the Stability of Collusion Strategic R&D Competition (4) Strategic R&D Competition (5) R&D Competition and Competitiveness in the Product Market (6) R&D Cooperation and Relative Performance

3. OT2010 3 Importance of Relative Performance

4. OT2010 4 relative profit maximization Consider quantity-setting competition (Cournot-type competition). Suppose that each firm maximizes relative profit (its own profit minus the rival’s profit) →Firms produce (more, less) aggressively.

5. OT2010 5 Equilibrium Consider quantity-setting competition (Cournot-type competition). Suppose that each firm maximizes relative profit (its own profit minus the rival’s profit) Homogeneous product market, symmetric firms. Firms 1 and 2 chooses their outputs Y 1 and Y 2 independently. P(Y):inverse demand function, C i : Firm i’s cost function F.O.C. P+P'Y 1 -C 1 ' -P'Y 2 =0 →At the symmetric equilibrium (Y 1 =Y 2 ), Price (>, ＝,<) marginal cost

6. OT2012 6 Vega-Redondo (1997) Consider quantity-setting competition (Cournot-type competition). Firms 1 and 2 chooses their outputs Y 1 and Y 2 independently. Homogeneous product market. No cost asymmetry. Firm choose the same output as the rival it the rival obtains the higher profit (Imitation) ＋ mutation →The Walrasian (perfectly competitive equilibrium outcome) is an evolutionally stable.

7. OT2012 7 Vega-Redondo (1997) The Walrasian (perfectly competitive equilibrium outcome) is an evolutionally stable. Intuition Relative profit is maximized at Walrasian equilibrium. Mutation (deviation form the Walrasian equilibrium) →Even if the profit of this mutant increases, the rival’s profit further increases→Imitation again yields Walrasian. Close relationship between evolution game and relative profit maximization.

8. OT2010 8 Relative profit, relative performance approach U 1 =π 1 -απ 2 α=1 perfect competition, α=0 Cournot, α=-1 Collusion We can analyze many situations, from perfect competition to collusion by a single simple model

9. OT2010 9 Relative profit, relative performance approach Examples of applications Cartel becomes more stable when α is smaller. (Matsumura and Matsushima, forthcoming) R&D level is non-monotone with respect to α, U-shaped (Today’s paper) An increase of α reduces innovation size and increases R&D expenditure The degree of product differentiation is decreasing in αwhen α is positive and not too small. When α is large or small, Multi-Store Paradox is solved.

10. OT2010 10 Rationalizations for relative performance approach (1) market evaluation for CEOs (2) evolutionary approach (3) envy, altruism (4) Fershtman and Judd (1987) (5) election, political science (6) status, macroeconomics (relative wage, relative consumption, relative wealth, relative income)

11. OT2010 11 Conjectural Variation conjectural variation Each firm chooses its output assuming that one unit increase of its output yields r unit increase of the total output. Cournot→r=1 Conjectural Variation Model is a general model including the Cournot model as a special case ( ？ ) Do the cases where r≠1 make sense?

12. OT2010 12 Conjectural Variation Model Suppose that r≠1. Firm 1’s output affects firm 2’s output. Thus, firm 2 must choose its output before firm 1’s choice. Firm 2’s output affects firm 1’s output. Thus, firm 1 must choose its output before firm 2’s choice. →Mutually inconsistent

13. OT2010 13 Why is this inconsistent model used by IO researchers? (1) an unmodeled dynamic model ～conjectural variation model analyzes a dynamic interaction between firms →If so, we should formulate a dynamic model rather than using an inconsistent static model (2) There exists models yielding the same solution →If so, we should use these model （３）This model represents various market structure with different degree of competition.

14. OT2010 14 Conjectural Variation Model の解 First-order condition in CV Model P+P'rＹ 1 =c First-order condition in Cournot Model P+P'Ｙ 1 =c →corresponds to the case of ｒ＝１. First-order condition in Bertrand Model ~ perfect competition, P =c →corresponds to the case of ｒ＝０ First-order condition in Joint Profit Maximization (collusion）, First-order condition in Joint Profit Maximization (collusion）, P+P'(Ｙ 1 +Ｙ 2 ) =c →corresponds to the case of ｒ＝２ A larger r represents a more severe competition.

15. OT2010 15 advantage of relative profit approach (1) Consistent model. (2) Foundation for any competitive structure between Bertrand and Collusion. (3) More realistic (I think).

16. OT2010 16 Stability of Collusion

17. OT2010 17 Prisoner’s Dilemma CD C(3,3)(0,4) D(4,0)(1,1) １ ２ Nash Equilibrium ： (D,D)

18. OT2010 18 Prisoner’s Dilemma and Cooperation We often observe cooperative behaviors under the situations of prisoner’s dilemma. Why ？ (1) Players are irrational. (2) Player’s payoff is different from what we observe (3) Long-run relationship→infinitely repeated game

19. OT2010 19 Idea of (2) ＣＤ C(3,3)(0,2) D(2,0)(1,1) １ ２ altruism Nash equilibrium :(C,C) (D,D)

20. OT2010 20 Idea of (3) ： infinitely repeated game Stage game is played repeatedly. Each player maximizes the discounted sum of the payoff obtained at the each stage game. Payoff at period 1+δ(payoff at period 2) +δ 2 (payoff at period 3)+δ 3 (payoff at period 4)+... δ ∈ (0,1) ： discount factor

21. OT2010 21 Interpretation of discount factor (1)Interest rate δ ＝ 1/(1 ＋ r) r ： interest rate (2)Subjective discount rate ~ indicates how important the future income is, indicates how patient the player is (3) The probability that the game continues until the next period ⇒ The probability that the game terminates within 10,000 years is almost 1. Infinitely repeated game never implies that the game never terminates. ~Much more realistic than what it seems at the first glance.

22. OT2010 22 subgame perfect Nash equilibrium The following strategies constitute a subgame perfect Nash equilibrium if and only if δ ≧ 1/3. Each player takes C at period t if and only if no player took D before period t. Otherwise each player takes D.

23. OT2010 23 The measure of the stability of collusion Collusion is sustainable if and only if δ ≧ δ*. → Collusion is more stable when δ* is smaller.

24. OT2010 24 Infinite Nash Reversion infinite Nash reversion (grim trigger strategy) If one player deviates from the collusion, then all play the one-shot Nash equilibrium thereafter. cf Optimal Penal Code

25. OT2010 25 Matsumura and Matsushima (forthcoming) ・ relative profit maximization approach ・ Investigate the relationship between α and δ*. If there is no collusion, a larger α indicates that firms face a more severe competition in the product market. If a larger α facilitates collusion, a larger α indicates less severe competition.

26. OT2010 26 Two effects The larger α is, the more severe competition after the deviation is. →more severe punishment ⇒ δ* can be decreasing in α. The larger α is, the deviation more effectively improve its payoff because deviation reduces the rival’s profit. ⇒ δ* can be increasing in α.

27. OT2010 27 Results δ* is increasing in α. This is true if we adopt optimal penal code. This is also true if we adopt price competition with product differentiation.

28. OT2010 28 R&D and Competition

29. OT2010 29 Two Views on Competition and R&D Monopoly View ~ Monopoly stimulates innovation ・ R&D investments are financed from monopoly profits ・ Monopolists internalize the spillover effects of R&D ・ R&D has economy of the scale Competition View ~ Competition stimulates innovation ・ Replacement effect (Arrow,1950) ・ Competitive pressure disciplines the management

30. OT2010 30 Brander and Spencer (1983) Two stage Strategic R&D game Cost-reducing R&D Cournot Competition No Spillovers

31. OT2010 31 Cournot Model Y１Y１ Reaction Curve of Firm 2 0 Ｙ２Ｙ２ Reaction Curve of Firm 1 Y1CY1C Y2CY2C

32. OT2010 32 Shift of Reaction Curve of Firm 1 through strategic R&D Y１Y１ Reaction Curve of Firm 2 0 Ｙ２Ｙ２ New Reaction Curve of Firm 1 Y1CY1C Y2CY2C

33. OT2010 33 Cost-Reducing Investments Model Duopoly, homogeneous goods market First stage: Each firm i independently chooses I i (R&D investment level), which affect its production costs. Second stage: After observing firms' production costs, firms face Cournot competition. Payoff: Π 1 =P(Y 1 +Y 2 )Y 1 -C 1 (I 1 )Y 1 -I 1

34. OT2010 34 backward induction Second stage ~ Cournot Competition Y 1 C (I 1,I 2 ), Y 2 C (I 2,I 1 ) Firm's output is increasing in its own investment and decreasing in the rival's investment. First stage ~ R&D Competition F.O.C. P'Y 1 (∂Y 1 C /∂I 1 + ∂Y 2 C /∂I 1 )+P ∂Y 1 C /∂I 1 -C 1 '(I 1 )Y 1 - C 1 ∂Y 1 C /∂I 1 -1=0

35. OT2010 35 First stage First Stage F.O.C. P'Y 1 (∂Y 1 C /∂I 1 + ∂Y 2 C /∂I 1 )+P∂Y 1 C /∂I 1 -C 1 '(I 1 )Y 1 - C 1 ∂Y 1 C /∂I 1 -1=0 P'Y 1 ∂Y 2 C /∂I 1 -C 1 '(I 1 )Y 1 -1=0 (envelope theorem) Cost-Minimizing Level -C 1 '(I 1 )Y 1 -1=0 Investment level exceeds cost minimizing level under strategic substitutes~ strategic effect

36. OT2010 36 Shifts of Reaction Curves Y１Y１ New Reaction Curve of Firm 2 0 Ｙ２Ｙ２ New Reaction Curve of Firm 1 Y1CY1C Y2CY2C Competition Reduces profits of Both firms

37. OT2010 37 This paper This paper We investigate the relationship between the strategic cost-reducing R&D investment and α. We investigate the relationship between the strategic cost-reducing R&D investment and α. Does competition accelerate R&D? Does envy society foster or deteriorate R&D?

38. OT2010 38 Two effects A larger α accelerates competition in the product market. →The equilibrium output is larger ⇒ A larger incentive for cost-reducing (Economy of the scale) A larger α reduces the degree of slope of the reaction curve at production stage. →Strategic effect of R&D becomes weaker

39. OT2010 39 Proposition 1 U-shaped relationship between R&D and α. Investment level is minimized when α ＝ 1/3. ・ Both monopoly and very competitive situation yields intensive R&D. This result support both competition view and monopoly view. ・ Introducing a small (large) degree of `envy’ into the standard Cournot competition reduces (increases) R&D. The opposite result to The opposite result to Aghion et al (2005).

40. OT2010 40 Joint Implementation Cooperation in R&D stage. Competition in production stage. R&D is decreasing in α. →If we consider joint implementation, severe competition reduces R&D.

41. OT2010 41 Oligopoly The same result is obtained if we consider the joint implementation. If we consider non-cooperative R&D, again similar result is obtained. However, the range of the decreasing part becomes wider. →If the number of firms is larger, competition more likely reduces R&D.

42. OT2010 42 Welfare Consider cooperative R&D. The equilibrium R&D level is too low for social welfare. Consider non-cooperative R&D. The equilibrium R&D level is too low for social welfare when α is large (small)