Game Theory Explained: A Mathematical Introduction With Optimization
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A01=Christopher H Griffin
Author_Christopher H Griffin
Battle of the Sexes
Bimatrix Game
Casino Games
Category=PBU
Category=PBUD
Chicken Game
Coalition Game
Cooperative Game
Cooperative Game Theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equilibrium
Evolutionary Game Theory
Extensive Form Game
Game Theory
Games Against The House
Linear Programming
Matrix Game
Nash Bargaining
Nash Equilibrium
Normal Form Game
Optimization
Prisoner's Dilemma
Probability Theory
Quadratic Programming
Replicator Equation
Rock-Paper-Scissors
Strategic Form Game
Utility Theory
Product details
- ISBN 9789819812875
- Publication Date: 20 Mar 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Paperback
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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.
