A course in stochastic game theory

Author(s)

    • Solan, Eilon

Bibliographic Information

A course in stochastic game theory

Eilon Solan

(London Mathematical Society student texts, 103)

Cambridge University Press, 2022

  • : hardback

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Note

Includes bibliographical references (p. 255-264) and index

Description and Table of Contents

Description

Stochastic games have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool - including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others - before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.

Table of Contents

  • Introduction
  • 1. Markov decision problems
  • 2. A Tauberian theorem and uniform -optimality in hidden Markov decision problems
  • 3. Strategic-form games - a review
  • 4. Stochastic games - the model
  • 5. Two-player zero-sum discounted games
  • 6. Semi-algebraic sets and the limit of the discounted value
  • 7. B-Graphs and the continuity of the limit $\lim_{\lambda \to 0} v_\lambda(s
  • q,r)$
  • 8. Kakutani's fixed-point theorem and multi-player discounted stochastic games
  • 9. Uniform equilibrium
  • 10. The vanishing discount factor approach and uniform equilibrium in absorbing games
  • 11. Ramsey's theorem and two-player deterministic stopping games
  • 12. Infinite orbits and quitting games
  • 13. Linear complementarity problems and quitting games
  • References
  • Index.

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Details

  • NCID
    BC14748865
  • ISBN
    • 9781316516331
  • LCCN
    2021055382
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge
  • Pages/Volumes
    ix, 267 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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