Econometrica: Mar, 1974, Volume 42, Issue 2

Non-Cooperative Equilibria in Time-Dependent Supergames

https://doi.org/0012-9682(197403)42:2<221:NEITS>2.0.CO;2-W
p. 221-238

James W. Friedman

This paper is concerned with "supergames" in which the action taken in a given time period by a player will affect the payoff to any other player in the subsequent period. A supergame consists of a set of players and a countable sequence of "ordinary" games. To illustrate "time-dependence," consider an economic market in discrete time. Say each firm must choose a price in each time period. This market has time-dependence if the amount demanded of a firm today is a function of the prices chosen today and of the prices chosen in the preceding period. Conditions are given for the existence of non-cooperative equilibria of two types: (i) steady state, in which the individual moves of the players converge over time to some s^0 and (ii) balance temptation equilibria of the sort developed by Friedman [6] for games lacking time dependence.