Stochastic
Games with Two Non-Absorbing States

Eilon Solan

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.