Game Theory Explained: A Mathematical Introduction with Optimization

Name: Game Theory Explained: A Mathematical Introduction with Optimization
Brand: World Scientific Publishing Company
SKU: 9789811297212
Price: 547.4 RON
Availability: InStock

Autor: GRIFFIN CHRISTOPHER

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Legare: Copertă tare

Editura: World Scientific Publishing Company

Disponibilitate: În depozitul extern

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

Informații despre carte

Autor

GRIFFIN CHRISTOPHER

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

2025

Pagini

270

EAN

9789811297212

ISBN

9811297215

Enbook ID

46708484

Editura

World Scientific Publishing Company

Greutate

575

Descriere completă

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.

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Game Theory Explained: A Mathematical Introduction with Optimization

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