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Game Theory, Alive

game theory , AliveAnna R. Karlin and Yuval PeresDecember 13, 2016 Please send comments and corrections to AMS. License or copyright restrictions may apply to redistribution; see to AMS. License or copyright restrictions may apply to redistribution; see overview of the book1 Part I: Analyzing games : Strategies and equilibria1 Part II: Designing games and mechanisms5 For the reader and instructor8 Prerequisites8 Courses8 Notes9 Part I: Analyzing games : Strategies and equilibria11 Chapter 1. Combinatorial Impartial Bouton s solution of Other impartial Partisan The game of Topology and Hex: A path of arrows* Hex and More general boards* Other partisan games played on graphs27 Notes31 Exercises32 Chapter 2. Two-person zero-sum The Minimax Theorem and its Simplifying and solving zero-sum Pure optimal strategies: Saddle Equalizing The technique of Using Nash equilibria, equalizing payoffs, and optimal A first glimpse of incomplete Proof of von Neumann s Minimax Theorem Zero-sum games with infinite action spaces 48iiiLicensed to AMS.

CONTENTS vii 14.9.3. A formula for the expected payment 255 14.9.4. The multibidder case 255 14.10. Approximately optimal auctions 258 14.10.1. The advantage of just one more bidder 258

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