A Course in Stochastic Game Theory
About this book
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.
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Information
Table of contents
- Cover
- Series information
- Title page
- Copyright information
- Dedication
- Contents
- Introduction
- 1 Markov Decision Problems
- 2 A Tauberian Theorem and Uniform ε-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[sub(λ→0)] v[sub(λ)](s;q,r)
- 8 Kakutani's Fixed-Point Theorem and Multiplayer 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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