A Course in Stochastic Game Theory (London Mathematical Society Student Texts, Series Number 103)

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. "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"--Back cover 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 "Stochastic games are a mathematical model that is used to study dynamic interactions among agents who in uence the evolution of the environment. These games were rst presented and studied by Lloyd Shapley (1953). Since Shapley's seminal work, the literature on stochastic games expanded considerably, and the model was applied to numerous areas, such as arm race, shery wars, and taxation". Sommario fornito dall'editore "Stochastic games are a mathematical model that is used to study dynamic interactions among agents who in uence the evolution of the environment. These games were rst presented and studied by Lloyd Shapley (1953).1;2 Since Shapley's seminal work, the literature on stochastic games expanded considerably, and the model was applied to numerous areas, such as arm race, shery wars, and taxation"-- Provided by publisher.