A course in stochastic game theory
著者
書誌事項
A course in stochastic game theory
（London Mathematical Society student texts, 103）
Cambridge University Press, 2022
- : pbk
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注記
Includes bibliographical references (p. 255-264) and index
内容説明・目次
内容説明
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.
目次
- 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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