ENGLISH

A Course in Stochastic Game Theory

By Eilon Solan

Book information

Publisher
Cambridge University Press
Year
2022
ISBN
1316516334, 9781316516331, 9781009029704, 2021055382, 2021055383, 9781009014793
Language
english
Format
PDF
Filesize
2 MB (2186180 bytes)
Series
London Mathematical Society Student Texts, Series Number 103
Edition
New
Pages
275\279
Time added
2023-01-19 23:37:08

Description

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. 01.0_pp_i_iv_Frontmatter 02.0_pp_v_vi_Dedication 03.0_pp_vii_x_Contents 04.0_pp_1_4_Introduction 05.0_pp_5_34_Markov_Decision_Problems 06.0_pp_35_48_A_Tauberian_Theorem_and_Uniform_-Optimality_in_Hidden_Markov_Decision_Problems 07.0_pp_49_54_Strategic-Form_Games_A_Review 08.0_pp_55_61_Stochastic_Games_The_Model 09.0_pp_62_81_Two-Player_Zero-Sum_Discounted_Games 10.0_pp_82_93_Semi-Algebraic_Sets_and_the_Limit_of_the_Discounted_Value 11.0_pp_94_110_B-Graphs_and_the_Continuity_of_the_Limit_lim0_sqr 12.0_pp_111_127_Kakutanis_Fixed-Point_Theorem_and_Multiplayer_Discounted_Stochastic_Games 13.0_pp_128_172_Uniform_Equilibrium 14.0_pp_173_194_The_Vanishing_Discount_Factor_Approach_and_Uniform_Equilibrium_in_Absorbing_Games 15.0_pp_195_210_Ramseys_Theorem_and_Two-Player_Deterministic_Stopping_Games 16.0_pp_211_235_Infinite_Orbits_and_Quitting_Games 17.0_pp_236_254_Linear_Complementarity_Problems_and_Quitting_Games 18.0_pp_255_264_References 19.0_pp_265_268_Index

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