The Cooperative Solution of Stochastic Games

by Elon Kohlberg & Abraham Neyman

Overview — In its broadest sense a stochastic game is one in which, at each stage, the game is in one of a finite number of states. Each player chooses an action from a finite set of possible actions. The players' actions and the state jointly determine a payoff to each player and transition probabilities to the succeeding state. While the theory of stochastic games has been developed in many different directions, there has been practically no work on the interplay between stochastic games and cooperative game theory. In this paper, building on the work of leading theorists such as Nash, Harsanyi, and Shapley, the authors take an initial step in this direction, defining a cooperative solution for strategic games and proving an existence theorem.

Author Abstract

Building on the work of Nash, Harsanyi, and Shapley, we define a cooperative solution for strategic games that takes account of both the competitive and the cooperative aspects of such games. We prove existence in the general non-transferable utility (NTU) case and uniqueness in the transferable utility (TU) case. Our main result is an extension of the definition and the existence and uniqueness theorems to stochastic games-discounted or undiscounted.