Game Theory Explained: A Mathematical Introduction With Optimization - Softcover

Griffin, Christopher H

Softcover

ISBN 10: 9819812879 ISBN 13: 9789819812875

Publisher: WSPC, 2025

Synopsis

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.

Edition details

• Publisher: WSPC
• Publication date: 2025
• Language: English
• ISBN 10: 9819812879
• ISBN 13: 9789819812875
• Binding: Paperback
• Number of pages: 306