@MISC{Vieille01two-playergames:, author = {Nicolas Vieille}, title = {Two-player games: a reduction}, year = {2001} }

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Abstract

The goal of this chapter, together with the next one, is to give a detailed overview of the proof of the following result. Theorem 1 Let Γ be a two-player stochastic game with Þnite action and states sets. The game Γ has a uniform equilibrium payoff. The complete proof is to be found in Vieille [4],[5]. The general idea of the proof is to deÞne a class of sets, the solvable sets, which can safely be thought of as absorbing states, and to construct ε-equilibrium proÞles such that the induced play reaches one of these sets with high probability, and remains there. Solvable sets are deÞned in Section 1. The organization of the proof is presented in Section 2. We shall use the tools introduced in a chapter by