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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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References

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  1. Takashi Kamihigashi & Santanu Roy, 2005. "Dynamic optimization with a nonsmooth, nonconvex technology: The case of a linear objective function," Discussion Paper Series 175, Research Institute for Economics & Business Administration, Kobe University.
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  14. Friedman, J. & Samuelson, L., 1991. "An Extension of the "Folk Theorem" with Continuous Reaction Functions," Discussion Paper 1991-21, Tilburg University, Center for Economic Research.
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  19. 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.
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  22. 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.
  23. 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.
  24. 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.
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  26. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  27. 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.
  28. Radner, Roy, 2003. "Viscous demand," Journal of Economic Theory, Elsevier, vol. 112(2), pages 189-231, October.
  29. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
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