© 2020

Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution

Discounted and Average Criteria


Table of contents

  1. Front Matter
    Pages i-xiv
  2. J. Adolfo Minjárez-Sosa
    Pages 1-8
  3. J. Adolfo Minjárez-Sosa
    Pages 9-29
  4. J. Adolfo Minjárez-Sosa
    Pages 31-46
  5. J. Adolfo Minjárez-Sosa
    Pages 69-94
  6. Back Matter
    Pages 95-120

About this book


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.


zero-sum Markov games Markov games difference-equation games probability measures and weak convergence stochastic kernels density estimation optimal strategies 91A15, 90C40, 62G05

Authors and affiliations

  1. 1.Department of MathematicsUniversity of SonoraHermosilloMexico

Bibliographic information

  • 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
  • Series Abbreviated Title SpringerBriefs in Probabil., Math.Statist.
  • DOI
  • Copyright Information The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-030-35719-1
  • eBook ISBN 978-3-030-35720-7
  • Series ISSN 2365-4333
  • Series E-ISSN 2365-4341
  • Edition Number 1
  • Number of Pages XIV, 120
  • Number of Illustrations 2 b/w illustrations, 2 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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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)