Noncooperative nonstationary stochastic games (Q1059562)

A stochastic non-stationary, non-cooperative game \(\{S_ n,X_ n,Y_ n,q_ n,u_ 1,u_ 2,n\in N\}\) is considered where the state spaces \(S_ n\) are countable and the players' action spaces \(X_ n\) and \(Y_ n\) are finite. Here, \((q_ n)\) is the sequence of transition probabilities depending on the history up to time \(n\in N\) and players' decisions, whereas \(u_ 1\) and \(u_ 2\) are bounded, continuous pay-off functions of two players depending on the infinite sequence of states and decisions. The aim of the paper is to prove an existence theorem for the equilibrium point for that game and to establish an approximation procedure for the game value by a sequence of finite horizon game values.