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Immediately Reactive Equilibria in Infinitely Repeated Games with Additively Separable Continuous Payoffs

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Author Info
Takashi Kamihigashi (Research Institute for Economics and Business Administration, Kobe University)
Taiji Furusawa (Hitotsubashi University)
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 the action of each player is a stationary function of the last action of the other player. We show that the set of IREs in the simultaneous move game is identical to that in the alternating move game. In both games, IREs are completely characterized in terms of indifference curves associated with what we call effective payoffs. A folk-type theorem using only IREs is established in a special case. Our results are applied to a prisoner's dilemma game with observable mixed strategies and a duopoly game. In the latter game, kinked demand curves with a globally stable steady state are derived.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp199.pdf
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Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 199.

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Length: 42 pages
Date of creation: Dec 2006
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Handle: RePEc:kob:dpaper:199

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  5. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-69, May. [Downloadable!] (restricted)
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  6. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
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  7. Friedman James W. & Samuelson Larry, 1994. "Continuous Reaction Functions in Duopolies," Games and Economic Behavior, Elsevier, vol. 6(1), pages 55-82, January. [Downloadable!] (restricted)
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  8. 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.
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  10. 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. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
  13. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October. [Downloadable!] (restricted)
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  14. Sen, Debapriya, 2004. "The kinked demand curve revisited," Economics Letters, Elsevier, vol. 84(1), pages 99-105, July. [Downloadable!] (restricted)
  15. Hans Haller & Roger Lagunoff, 2006. "Markov Perfect Equilibria in Repeated Asynchronous Choice Games," Levine's Bibliography 321307000000000560, UCLA Department of Economics. [Downloadable!]
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  16. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December. [Downloadable!] (restricted)
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