Zero-sum discrete-time Markov games with unknown disturbance distribution : discounted and average criteria /

Zero-sum discrete-time Markov games with unknown disturbance distribution : discounted and average criteria /

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Bibliographic Details
Author / Creator:	Minjárez-Sosa, J. Adolfo.
Imprint:	Cham : Springer, 2020.
Description:	1 online resource
Language:	English
Series:	SpringerBriefs in probability and mathematical statistics SpringerBriefs in probability and mathematical statistics.
Subject:	Markov processes. Differential games. Differential games. Markov processes.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12603451

Hidden Bibliographic Details
ISBN:	9783030357207 3030357201 3030357198 9783030357191
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index.
Summary:	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 statistical estimation and control techniques for the construction of strategies of the players are introduced, with illustrative examples. In this sense, the book is an essential reference for theoretical and applied researchers in the fields of stochastic control and game theory, and their applications.
Other form:	Print version: Minjárez-Sosa, J. Adolfo. Zero-sum discrete-time Markov games with unknown disturbance distribution. Cham : Springer, 2020 3030357198 9783030357191
Standard no.:	10.1007/978-3-030-35 10.1007/978-3-030-35720-7

Description
Summary:	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 statistical estimation and control techniques for the construction of strategies of the players are introduced, with illustrative examples. In this sense, the book is an essential reference for theoretical and applied researchers in the fields of stochastic control and game theory, and their applications.
Physical Description:	1 online resource
Bibliography:	Includes bibliographical references and index.
ISBN:	9783030357207 3030357201 3030357198 9783030357191