Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution
Discounted and Average Criteria
Authors: Minjárez-Sosa, J. Adolfo
Free Preview- First book providing a study on discrete-time Markov games with unknown disturbance distribution
- Presents a systematic analysis on recent developments of estimation and control procedures in Markov games
- Contains several examples to illustrate the game models as well as the implementation of the estimation and control algorithms
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- About this book
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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.
- Reviews
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“This is a well written book that maintains a balance between theory and numerical examples. Each chapter is interesting and useful for the readers. This book can be recommended as a valuable material for both self study and teaching purposes, but because of its rigorous style it works also as a valuable reference for research purposes.” (Samir Kumar Neogy, zbMATH 1454.91004, 2021)
- Table of contents (5 chapters)
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Zero-Sum Markov Games
Pages 1-8
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Discounted Optimality Criterion
Pages 9-29
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Average Payoff Criterion
Pages 31-46
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Empirical Approximation-Estimation Algorithms in Markov Games
Pages 47-67
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Difference-Equation Games: Examples
Pages 69-94
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution
- Book Subtitle
- Discounted and Average Criteria
- Authors
-
- J. Adolfo Minjárez-Sosa
- Series Title
- SpringerBriefs in Probability and Mathematical Statistics
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-35720-7
- DOI
- 10.1007/978-3-030-35720-7
- Softcover ISBN
- 978-3-030-35719-1
- Series ISSN
- 2365-4333
- Edition Number
- 1
- Number of Pages
- XIV, 120
- Number of Illustrations
- 2 b/w illustrations, 2 illustrations in colour
- Topics
