Repeated Games with Absorbing States
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  and by Thuijsman . Several examples will illustrate the proof.
KeywordsStationary Strategy Stochastic Game Repeated Game Average Reward Small Triangle
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