Abstract
In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.
Highlights
The class of stochastic games was initially introduced by L
We have constructed a model of cooperative stochastic games with mean-variance preferences
We have defined a cooperative stochastic game with mean-variance preferences in the form of characteristic function determined by a maxmin approach
Summary
The class of stochastic games was initially introduced by L. He considered two-player zero-sum stochastic games with finite state space and finite strategy spaces and proved the existence of optimal stationary strategies when players’ payoff function is discounted mathematical expected payoff. The expected discounted payoff is considered as a measure of a player’s payoff in a stochastic game In this case, it is supposed that the players are risk neutral. A mean-variance stochastic game in discrete time with the payoff function, which is a linear combination of expectation and standard deviation of the payoff, is proposed. We consider a non-cooperative stochastic game with mean-variance utility function. The goal of the paper is to propose a scheme of construction of a cooperative version of a stochastic game, in which expectation and standard deviation of players’. The proofs of all propositions are given in the appendix
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