Stochastic Games with Two Non-Absorbing States
Israel Journal of Mathematics 119 (2000), 29-54.
We consider recursive games that satisfy an absorbing property defined by Vieille (Israel Journal of Mathematics, 2000).
We give two sufficient conditions for existence of an equilibrium payoff in such games, and prove that if the game has at most two non-absorbing states, then at least one of the conditions is satisfied.
Using a reduction of Vieille (Israel Journal of Mathematics, 2000), we conclude that every stochastic game that has at most two non-absorbing states admits an equilibrium payoff.