On the existence and uniqueness of equilibrium situations in Markovian games with discounting (Q5942122)

In the paper it is proved: Every two-person zero-sum Markov game with finitely many states and finitely many, possibly state-dependent actions, with infinite horizon and proper discounting has a value vector and optimal stationary, in general randomized strategies for both players. Essential tools for the proof are Banach's fixed-point theorem, the approximation of the game by a sequence of those with finite horizon and Tikhonov's continuity theorem. The problem of uniqueness is reduced to that of matrix games. Although a part of results is already known, the paper has survey character and is nice to read. Markov decision processes are special Markov games, their treatment is of greater detail than it would be necessary. The list of references does not contain newer work but some remarkable papers from game theory and analysis what is fully sufficient.