A Course in Stochastic Game Theory

ISBN-13: 9781009014793 / Angielski / Miękka / 2022 / 275 str.

Eilon (Tel-Aviv University) Solan

Opis

This book for beginning graduate students presents a course on stochastic games and the mathematical methods used in their analysis.

Recenzje

'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

Spis treści

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.