Zerosum Discretetime Markov Games With Unknown Disturbance Distribution

This SpringerBrief deals with a class of discrete-time zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs, under discounted and average criteria, whose state process evolves according to a stochastic difference equation. The corresponding disturbance process is an observable sequence of independent and identically distributed random variables with unknown distribution for both players. Unlike the standard case, the game is played over an infinite horizon evolving as follows. At each stage, once the players have observed the state of the game, and before choosing the actions, players 1 and 2 implement a statistical estimation process to obtain estimates of the unknown distribution.

This SpringerBrief deals with a class of discrete-time zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs, under discounted and average criteria, whose state process evolves according to a stochastic difference equation. The corresponding disturbance process is an observable sequence of independent and identically distributed random variables with unknown distribution for both players. Unlike the standard case, the game is played over an infinite horizon evolving as follows.

With the first edition out of print, we decided to arrange for republi­ cation of Denumerrible Markov Ohains with additional bibliographic material. The new edition contains a section Additional Notes that indicates some of the developments in Markov chain theory over the last ten years.

In this revised edition I have added some new material as well as making corrections and improvements. In Part I the additions (in §§ 9, 10, 11) are a few results closely related to the original text and illustrative of the method of taboos. In Part II the major additions have to do with the boundary theory; these include "fine topology" in § 11, "Martin boundary" and "entrance law" in § 19. The old Addenda have been expanded into the new § 12, some of the developments there being also germane to the boundary theory. It is hoped that these efforts have now brought the reader right up to the edge of the boundary. A number of selected items have been inserted in the Bibliography as a further guide to the latest literature on the above-mentioned and other topics.

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