Game Theory, Alive

This book is a wide-ranging survey of game theory, combining rigorous mathematics with plenty of motivation, examples and illustrations. After a chapter on combinatorial games, the authors introduce zero-sum games and prove the minimax theorem in Chapter 2.
This is followed by examples of games on graphs including search games in chapter 3. Nash equilibrium is introduced in Chapter 4 with multiple examples; its existence is proved in the next chapter via fixed point theorems. Chapters 6-8 concern extensions of the theory, in particular the notion evolutionary stable equilibria shows the interplay of game theory and mathematical biology.
Chapter 10 and 11 study different notions of fair allocation: the Gale-Shapley stable marriage algorithm and cake cutting. The elegant and practically important topic of auctions is the subject of Chapters 14-15, while Chapter 16 studies scoring rules: how do you pay forecasters to motivate them to provide the best forecasts they can? The final chapter introduces the fruitful interaction of game theory and online learning. Appendixes provide necessary background on linear programming, convex functions and probability. The book has been class tested in both undergraduate and graduate classes at many universities, including UC Berkeley, MIT, University of Washington, and UBC.

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