RECURSIVE REPEATED GAMES WITH ABSORBING STATES

We show the existence of stationary limiting average epsilon-equilibri a (epsilon > 0) for two-person recursive repeated games with absorbing states. These are stochastic games where all states but one are absor bing, and in the nonabsorbing state ail payoffs are equal to zero. A s tate is called absorbing if the probability of a transition to any oth er state is zero for all available pairs of actions. For the purpose o f our proof, we introduce properness for stationary strategy pairs. Ou r result is sharp since it extends neither to the case with more nonab sorbing states, nor to the n-person case with n > 2. Moreover, it is w ell known that the result cannot be strengthened to the existence of 0 -equilibria and that repeated games with absorbing states generally do not admit stationary epsilon-equilibria.