02696nam a22002897a 4500 55777 55777 20191021151347.0 191021b ||||| |||| 00| 0 eng d 9781470454784 519.3 KAR Karlin, Anna R Game theory, alive / Anna R Karlin Providence, Rhode Island : American Mathematical Society, ©2017 xxvi, 372 pages : illustrations chiefly color ; 27 cm Part I. Analyzing games : strategies and equilibria. Combinatorial games -- Two-person zero-sum games -- Zero-sum games on graphs -- General-sum games -- Existence of Nash equilibria and fixed points -- Games in extensive form -- Evolutionary and correlated equilibria -- The price of anarchy -- Random-turn games -- Part II. Designing games and mechanisms. Stable matching and allocation -- Fair division -- Cooperative games -- Social choice and voting -- Auctions -- Truthful actions in win/lose settings -- VCG and scoring rules -- Matching markets -- Adaptive decision making -- Appendix A. Linear programming -- Appendix B. Some useful probability tools. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science, economics, social choice, biology, and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics."--Back cove Mathematics Probabilities & applied mathematics Game theory. Game theory, economics, social and behavioral sciences -- Game theory -- Cooperative games. Game theory, economics, social and behavioral sciences -- Game theory -- Games involving graphs Game theory, economics, social and behavioral sciences -- Mathematical economics -- Market models (auctions, bargaining, bidding, selling, Mathematisches Spiel Game theory, economics, social and behavioral sciences -- Game theory Karlin, Anna R.; Peres, Yuval BOOK