Zero-Sum Average Semi-Markov Games: Fixed-Point Solutions of the Shapley Equation

Óscar Vega-Amaya

36 citations0/0 files storedSIAM Journal on Control and Optimization

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Game Theory and Applications Game Theory and Voting Systems Adaptive Dynamic Programming Control

Abstract

This paper deals with zero-sum average semi-Markov games with Borel state and action spaces, unbounded payoffs, and mean holding times. A solution to the Shapley equation is obtained via the Banach fixed-point theorem assuming that the model satisfies a Lyapunov-like condition, a growth hypothesis on the payoff function, and the mean holding times, besides standard continuity and compactness requirements.

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References

1996Competitive Markov Decision Processes 1953Minimax Theorems 1997Contraction Conditions for Average and α-Discount Optimality in Countable State Markov Games with Unbounded Rewards 1985Measurable Selection Theorems for Minimax Stochastic Optimization Problems 2000Zero-Sum Stochastic Games in Borel Spaces: Average Payoff Criteria 1999Optimal strategies in a class of zero-sum ergodic stochastic games 2002Zero-Sum Semi-Markov Games

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2007Zero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffs

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