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Global Dynamics in Repeated Games with Additively Separable Payoffs

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  • Takashi Kamihigashi

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

  • Taiji Furusawa

    (Graduate School of Economics, Hitotsubashi University, Tokyo, Japan)

Abstract

This paper studies the global dynamics of a class of infinitely repeated two-player games 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 is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. 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/DP2010-04.pdf
File Function: Revised version, 2010
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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 DP2010-04.

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Length: 38 pages
Date of creation: Feb 2010
Date of revision: Jun 2010
Handle: RePEc:kob:dpaper:dp2010-04

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Related research

Keywords: Immediately reactive equilibria; Additively separable payoffs; Kinked demand; Gradual cooperation; Prisoners' dilemma;

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References

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  1. Haller, Hans & Lagunoff, Roger, 2010. "Markov Perfect equilibria in repeated asynchronous choice games," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1103-1114, November.
  2. Taiji Furusawa, 2001. "Threats and Concessions in Tariff Settings," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-123, Boston University - Department of Economics.
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Cited by:
  1. Takashi Kamihigashi, 2013. "Elementary Results on Solutions to the Bellman Equation of Dynamic Programming:Existence, Uniqueness, and Convergence," Discussion Paper Series DP2013-35, Research Institute for Economics & Business Administration, Kobe University, revised Dec 2013.
  2. Taiji Furusawa & Takashi Kamihigashi, 2012. "Threats Or Promises? A Built-In Mechanism Of Gradual Reciprocal Trade Liberalization," The Japanese Economic Review, Japanese Economic Association, vol. 63(2), pages 259-279, 06.

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