Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2005-19 December 2005

The Structure of Non-zero-sum Stochastic Games

Robert Simon

Strategies in a stochastic game are delta perfect if the induced one stage games have certain delta equilibrium properties. Sufficient conditions are proven for the existence of delta perfect strategies for all delta > 0 implying the existence of epsilon equilibria for every epsilon > 0. Using this approach we prove the existence of epsilon equilibria for every epsilon for a special class of quitting games. The important technique of the proof belongs to algebraic topology and reveals that more general proofs for the existence of epsilon equilibria in stochastic games must involve the topological structure of how the equilibria of one stage games are related to changes in the payoffs.

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Last modified: 12th December 2005