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Game Theory Explained: A Mathematical Introduction with Optimization

Name: Game Theory Explained: A Mathematical Introduction with Optimization
Brand: World Scientific Publishing Company
SKU: 46708484
Price: 98.82 EUR
Availability: InStock
Author: GRIFFIN CHRISTOPHER
ISBN: 9789811297212

GRIFFIN CHRISTOPHER

Jazyk

Angličtina

Kniha Pevná

Libristo kód: 46708484

Nakladateľstvo World Scientific Publishing Company, február 2025

This book provides an introduction to the mathematical theory of games using both classical methods... Celý popis

Libristo kód: 46708484

239 b

98.82 €

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This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.

Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash's proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a "bonus" appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author's particular area of study.