Explicit Formulas for Repeated Games with Absorbing States

Explicit formulas for the asymptotic value and the asymptotic minmax of finite discounted absorbing games are provided. New simple proofs for the existence of the limits when the players are more and more patient (i.e. when the discount factor goes zero) are given. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact action sets and jointly continuous payoff functions