6 - A non-cooperative equilibrium for supergames

Summary

Introduction

John Nash has contributed to game theory and economics two solution concepts for nonconstant sum games. One, the non-cooperative solution [9], is a generalization of the minimax theorem for two person zero sum games and of the Cournot solution; and the other, the cooperative solution [10], is completely new. It is the purpose of this paper to present a non-cooperative equilibrium concept, applicable to supergames, which fits the Nash (non-cooperative) definition and also has some features resembling the Nash cooperative solution. “Supergame” describes the playing of an infinite sequence of “ordinary games” over time. Oligopoly may profitably be viewed as a supergame. In each time period the players are in a game, and they know they will be in similar games with the same other players in future periods.

The most novel element of the present paper is in the introduction of a completely new concept of solution for non-cooperative supergames. In addition to proposing this solution, a proof of its existence is given. It is also argued that the usual notions of “threat” which are found in the literature of game theory make no sense in non-cooperative supergames. There is something analogous to threat, called “temptation,” which does have an intuitive appeal and is related to the solution which is proposed.

In section II the ordinary game will be described, the non-cooperative equilibrium defined and its existence established. Section III contains a description of supergames and supergame strategies.