A Course in Stochastic Game Theory

Erscheinungsjahr 2022
ISBN: 978-1-316-51633-1
Verlag: Cambridge University Press

Buch, Englisch, Band 103, 275 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 606 g

Reihe: London Mathematical Society Student Texts

Stochastic games are 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.

Autoren/Hrsg.

Solan, Eilon

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Risikobewertung, Risikotheorie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Mikroökonomie

Inhaltsverzeichnis

Introduction; 1. Markov decision problems; 2. A Tauberian theorem and uniform e-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.

Über Autor(innen)

Solan, Eilon
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.