Perfect information two-person zero-sum markov games with imprecise transition probabilities

초록

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293-302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.

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