Title
Global Dynamics in Repeated Games with Additively Separable Payoffs
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 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 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 payoffs;
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