Solvable states in stochastic games (Q2366103)

The paper deals with a non-zero-sum two-person undiscounted stochastic game \(\Gamma\), with a finite set of states and with finite sets of players' actions. It is shown that there exist the so-called solvable states with the following property: for each \(\varepsilon> 0\) the game \(\Gamma\), starting from any solvable state, has \(\varepsilon\)-equilibrium strategies in the sense that they constitute an \(\varepsilon\)-Nash equilibrium in all the subgames of \(\Gamma\) of the first \(n\) steps, for sufficiently large \(n\). The second result is that the considered stochastic game has an equilibrium payoff when the number of states is less than 4.