Strategic support of the Shapley value in stochastic games

Abstract

We consider the cooperative behavior in stochastic games. We assume that players cooperate in the game and agree on realizing the Shapley value as an imputation of their total payoff. The problem of subgame (time) consistency of the Shapley value is examined. The imputation distribution procedure is constructed to make the Shapley value subgame consistent. We redefine the payoffs in stochastic game applying the imputation distribution procedure. The problem of strategic support of the Shapley value is examined. We prove that the cooperative strategy profile is the Nash equilibrium in the stochastic game with re-defined payoff functions when some conditions are satisfied. The theoretical results are demonstrated on the example of a data transmission game for a wireless network of a specific topology.