Perfect information two-person zero-sum Markov games with imprecise transition probabilities
Basing on an extension of the controlled Markov set-chain model by \textit{M. Kurano, M. Hosaka, Y. Huang} and \textit{J. Song} [J. Appl. Probab. 35, No. 2, 293--302 (1998; Zbl 0911.90344)] into a competitive two-player game setting, this paper provides a model of perfect information two-player zero-sum Markov games with imprecise transition probabilities. By introducing an equilibrium value for the games formulated with the model in terms of a partial order, this paper establishes the existence of an equilibrium policy pair that achieves the equilibrium value. Moreover, finite-approximation error bounds obtained from a value iteration-type algorithm are analyzed, and some applications of the model are discussed.
scientific article; zbMATH DE number 5082016