Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs

Takashi Kamihigashi and Taiji Furusawa

No 210, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe 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 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.

Keywords: Immediately reactive equilibria; Additively separable pay-offs; Kinked demand; Gradual cooperation; Prisoners'dilemma (search for similar items in EconPapers)
Pages: 45 pages
Date: 2007-11
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