This book presents a course on stochastic games and the mathematical methods used in their analysis. Assuming only basic undergraduate mathematics, it includes numerous examples and exercises, with solutions available online, making it suitable for beginning graduate students and newcomers from other areas of mathematics and game theory.
This book presents a course on stochastic games and the mathematical methods used in their analysis. Assuming only basic undergraduate mathematics, it includes numerous examples and exercises, with solutions available online, making it suitable for beginning graduate students and newcomers from other areas of mathematics and game theory.
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.
Inhaltsangabe
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.
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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