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Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs

Author

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  • 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.

Suggested Citation

  • Takashi Kamihigashi & Taiji Furusawa, 2007. "Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 210, Research Institute for Economics & Business Administration, Kobe University.
  • Handle: RePEc:kob:dpaper:210
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    File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp210.pdf
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    References listed on IDEAS

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    Keywords

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

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