Repeated Games with Absorbing States

Abstract

In this paper we shall present a proof for the existence of limiting average ε-equilibria in non-zero-sum repeated games with absorbing states, i.e., stochastic games in which all states but one are absorbing. We assume that the action spaces shall be finite; hence there are only finitely many absorbing states. A limiting average ε-equilibrium is a pair of strategies (σ _ε , τ _ε , with ε > 0, such that for all σ and τ we have γ₁(σ, τ _ε ) ≤ γ₁(σ _ε , τ _ε ) + ε and γ₂(σ _ε ,τ) ≤ γ₂(σ _ε τ _ε ) + ε. The proof presented in this chapter is based on the publications by Vrieze and Thuijsman [7] and by Thuijsman [5]. Several examples will illustrate the proof.