Game Theory and Strategy, Volume 36"This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals—or companies, or political parties, or nations--confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology. In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like 'fairness' are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations."-- |
Contents
Guerrillas Police and Missiles | 5 |
Games Against Nature | 56 |
12 | 65 |
Trust Suspicion | 81 |
Evolutionarily Stable Strategies | 93 |
The Nash Arbitration Scheme and Cooperative Solutions | 102 |
ManagementLabor Arbitration | 112 |
The Duopoly Problem | 118 |
Prisoners Dilemma | 145 |
Pathan Organization | 161 |
Bargaining Sets | 190 |
The Shapley Value | 207 |
Cost Allocation in India | 209 |
Answers to Exercises | 225 |
The ShapleyShubik | 239 |
241 | |
Other editions - View all
Common terms and phrases
arbitration scheme Athena axioms Banzhaf index bargaining set bloc Blues calculate cardinal utilities characteristic function form choice choose coalition structure Colin plays column consider cooperation core counter-prudential Divide-the-Dollar dominant strategy entry equilibrium example Exercises for Chapter expected payoff expected value Figure game theory game tree Gately point give grand coalition Guerrillas hawk Hence idea imputation information set largest Larry Mathematical matrix game method minimal winning minimax mixed strategy movement diagram n-person games n-tuple Nash arbitration Nash equilibrium Neumann nodes non-zero-sum games nucleolus outcome Pareto optimal payoff polygon players play possible predict preferences Prisoner's Dilemma problem proposed Rapoport rational result Rose and Colin Rose's saddle point security level Shapley value Shapley-Shubik power index situation solution stable set status quo point Straffin Suppose take both boxes theorem threat strategies v(AB v(ABC v(AC v(BC valid counter-objection villages voters winning coalition zero-sum game Zeus