Title
Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs
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
Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: (81) 78 803 7036
Fax: (81) 78 803 7059
Taiji FURUSAWA
Graduate School of Economics, Hitotsubashi University