Pure and mixed stationary equilibria for dynamic positional games on graphs [Articol]

Abstract

A class of m-player dynamic positional games on graphs that extends the two-player zero-sum mean payoff games on graphs is formulated and studied. We consider dynamic positional games with average and discounted payoffs criteria for the players. We show that for an arbitrary game with average payoffs there exists Nash equilibrium in mixed stationary strategies and for an arbitrary two-player zero-sum average positional game there exists Nash equilibrium in pure stationary strategies. Additionally we show that for an arbitrary dynamic positional game with discounted payoffs there exists a Nash equilibrium in pure stationary strategies. Some approaches for determining the optimal stationary strategies of the players in such games are proposed.