Zero-Sum Semi-Markov Games

Anna Jaśkiewicz

37 citations0/0 files storedSIAM Journal on Control and Optimization

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Game Theory and Applications Probability and Statistical Research Adaptive Dynamic Programming Control

Abstract

This paper deals with Borel state and action spaces zero-sum semi-Markov games under the expected long run average payoff criterion. The transition probabilities are assumed to satisfy some generalized geometric ergodicity conditions. The main result states that the optimality equation has a solution, which is approximated by the solutions of some $\varepsilon$-perturbed semi-Markov games. As a corollary, the existence of value and average optimal strategies for the players is established.

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References

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 1995Zero-sum Markov games and worst-case optimal control of queueing systems 1999Optimal strategies in a class of zero-sum ergodic stochastic games

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2003Zero-Sum Average Semi-Markov Games: Fixed-Point Solutions of the Shapley Equation 2007Zero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffs

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