Del 103 i serien London Mathematical Society Student Texts

A Course in Stochastic Game Theory

Inbunden, Engelska, 2022

AvEilon Solan

1 529 kr

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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.

Produktinformation

Utgivningsdatum2022-05-26
Mått158 x 235 x 20 mm
Vikt570 g
FormatInbunden
SpråkEngelska
SerieLondon Mathematical Society Student Texts
Antal sidor278
FörlagCambridge University Press
ISBN9781316516331

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Eilon Solan is the Nathan and Lily Silver Chair in Stochastic Models in the School of Mathematical Sciences at Tel Aviv University. He has more than 20 years' experience of teaching and research in stochastic games and he co-authored the undergraduate textbook Game Theory (Cambridge, second edition 2020). Professor Solan is also Founder and Director of the Good to Know project, which aims to make important ideas in science accessible to children and adolescents.

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 $\lim_{\lambda \to 0} v_\lambda(s;q,r)$; 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.

'The book presents a course on the theory of stochastic games. It is self-contained and accessible at an undergraduate level. Instead of seeking the most general results and the broadest spectrum of knowledge in the field, the author prefers firstly to focus with great care on the most central aspects of the theory and then analyses more specifically some particular classes of stochastic games.' Catherine Rainer, zbMATH