Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution : Discounted and Average Criteria. 1st ed. 2020

種類:

電子ブック

責任表示:

by J. Adolfo Minjárez-Sosa

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Minjárez-Sosa, J. Adolfo.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Probability and Mathematical Statistics ;

ISBN:

9783030357207 [3030357201]    

注記:

Zero-sum Markov games -- Discounted optimality criterion -- Average payoff criterion -- Empirical approximation-estimation algorithms in Markov games -- Difference-equation games: examples -- Elements from analysis -- Probability measures and weak convergence -- Stochastic kernels -- Review on density estimation. .
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. Then, independently, the players adapt their decisions to such estimators to select their actions and construct their strategies. This book presents a systematic analysis on recent developments in this kind of games. Specifically, the theoretical foundations on the procedures combining statistic

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