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Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs

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Author Info

  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Taiji Furusawa

    (Graduate School of Economics, Hitotsubashi University, Japan)

Abstract

This paper studies a class of infinitely repeated games with two players in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in their actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action in each period is a stationary function of the other player's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. In a special case we establish a folk-type theorem using only IREs that are continuous and punish deviations in a minimal way. Our results are used to show that in a prisoners' dilemma game with observable mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp210.pdf
File Function: First version, 2007
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 210.

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Length: 45 pages
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:kob:dpaper:210

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Related research

Keywords: Immediately reactive equilibria; Additively separable pay-offs; Kinked demand; Gradual cooperation; Prisoners'dilemma;

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  1. Hans Haller & Roger Lagunoff, 2006. "Markov Perfect Equilibria in Repeated Asynchronous Choice Games," Levine's Bibliography 321307000000000560, UCLA Department of Economics.
  2. Roger Lagunoff & Akihiko Matsu, . "Asynchronous Choice in Repeated Coordination Games," Penn CARESS Working Papers 23a1aa461811b8f48b0334f6e, Penn Economics Department.
  3. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  4. Kranton, Rachel E, 1996. "The Formation of Cooperative Relationships," Journal of Law, Economics and Organization, Oxford University Press, vol. 12(1), pages 214-33, April.
  5. Stahl, Dale II, 1991. "The graph of Prisoners' Dilemma supergame payoffs as a function of the discount factor," Games and Economic Behavior, Elsevier, vol. 3(3), pages 368-384, August.
  6. Friedman, J.W. & Samuelson, L., 1988. "Subgame Perfect Equilibrium With Continuous Reaction Functions," Papers 4-88-3, Pennsylvania State - Department of Economics.
  7. Friedman James W. & Samuelson Larry, 1994. "An Extension of the Folk Theorem with Continuous Reaction Functions," Games and Economic Behavior, Elsevier, vol. 6(1), pages 83-96, January.
  8. Watson, Joel, 1999. "Starting Small and Renegotiation," Journal of Economic Theory, Elsevier, vol. 85(1), pages 52-90, March.
  9. Yoon, Kiho, 2001. "A Folk Theorem for Asynchronously Repeated Games," Econometrica, Econometric Society, vol. 69(1), pages 191-200, January.
  10. Friedman, James W, 1973. "On Reaction Function Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 721-34, October.
  11. Radner, Roy, 2003. "Viscous demand," Journal of Economic Theory, Elsevier, vol. 112(2), pages 189-231, October.
  12. Friedman, James W, 1976. "Reaction Functions as Nash Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 43(1), pages 83-90, February.
  13. J. Tirole & E. Maskin, 1982. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large-Fixed Costs," Working papers 320, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Friedman, J.W. & Samuelson, L., 1990. "Continuous Reaction Functions In Duopolies," Working papers 90-25, Wisconsin Madison - Social Systems.
  15. Takashi Kamihigashi & Santanu Roy, 2006. "Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function," Economic Theory, Springer, vol. 29(2), pages 325-340, October.
  16. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  17. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  18. Sen, Debapriya, 2004. "The kinked demand curve revisited," Economics Letters, Elsevier, vol. 84(1), pages 99-105, July.
  19. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
  20. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  21. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
  22. Stanford, William G., 1986. "Subgame perfect reaction function equilibria in discounted duopoly supergames are trivial," Journal of Economic Theory, Elsevier, vol. 39(1), pages 226-232, June.
  23. Furusawa, Taiji & Kawakami, Toshikazu, 2008. "Gradual cooperation in the existence of outside options," Journal of Economic Behavior & Organization, Elsevier, vol. 68(2), pages 378-389, November.
  24. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
  25. Langlois, Jean-Pierre P. & Sachs, Jonathan A., 1993. "Existence and local stability of Pareto superior reaction function equilibria in discounted supergames," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 199-221.
  26. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May.
  27. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
  28. Kalai, Ehud & Samet, Dov & Stanford, William, 1988. "A Note on Reactive Equilibria in the Discounted Prisoner's Dilemma and Associated Games," International Journal of Game Theory, Springer, vol. 17(3), pages 177-86.
  29. Robson, Arthur J, 1986. "The Existence of Nash Equilibria in Reaction Functions for Dynamic Models of Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(3), pages 539-44, October.
  30. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  31. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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