Cooperative solutions for TU and NTU stochastic game-theoretical approach

Abstract

The player's payoff in stochastic games is a stochastic variable. In most studies, predicted payout is referred to as a payoff, implying that the players are risk averse. However, there may be risk-averse players that consider "risk" while calculating their stochastic payoffs. We offer a model of stochastic games using mean-variance reward functions, which are the sum of expectation and standard deviation multiplied by a coefficient indicating a player's risk aversion. By adopting a maxmin technique to define the characteristic function, we may create a cooperative version of a stochastic game with mean-variance preferences. This paper contains an analysis of a cooperative solution concept of stochastic games for both TU (transferable utility) and NTU (non-transferable utility) games. We proposed a cooperative game solution method of extension of two-person zero sum strategic game to n-agent stochastic stage game using both Shapley and Banzhaf index functions. Results are proved for both discounted and undiscounted payoff situations. Existing models of discrete-time stochastic games and ways to finding cooperative solutions in these games are extended in this study.