Game Theory Explained

A Mathematical Introduction With Optimization

Christopher H Griffin (The Pennsylvania State University, Usa)

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English

World Scientific Publishing Co Pte Ltd
20 March 2025

Optimisation; Game theory

Summary
Details

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.

By: Christopher H Griffin (The Pennsylvania State University Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789819812875
ISBN 10: 9819812879
Pages: 308
Publication Date: 20 March 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active