Theory of Games

This introduction to game theory aims to present a concise account of the fundamental concepts of the subject and to develop themes such as continuous games and n-person (multi-user) non co-operative and co-operative games. The first part of the book is devoted to the properties of matrix games, and two elementary proofs of the Minimax theorem are given. Professor Wang then considers the theory and applications of continuous games and n-person non-co-operative games. The book culminates in a comprehensive treatment of n-person co-operative games and includes an introduction to the nucleolus concept. Undergraduate and graduate students of mathematics and related subjects should find this a readable first account of the subject and it may be of interest also to research workers requiring a concise introduction to key topics.Table of ContentPart 1 Matrix games: introduction; matrix games; saddle points; mixed strategies; the Minimax theorem; inductive proof of the Minimax theorem; saddle points in mixed strategies; optimal strategies and their properties; domination of strategies; solution of 2 x 2 matrix games; graphical solution of 2 x n and m x 2 matrix games; solution of 3 x 3 matrix games; matrix games and linear programming. Part 2 Continuous games: zero-sum two-person infinitive games; mixed strategies; continuous games; properties of optimal strategies; convex games; separable games; an example of a game of timing. Part 3 N-person non-co-operative games: introduction; existence of equilibrium point - Nash's theorem; equilibrium points of 2 x 2 bimatrix games. Part 4 N-person co-operative games: introduction; properties of characteristic functions; imputations; strategic equivalence and (0.1) normalization; two-person co-operative games; domination of imputations - three person co-operative games; the core of a co-operative game; stable sets of co-operative games; pre-imputations and strong E-cores; the kernel of a co-operative game; the nucleolus of a co-operative game; shapley value. References. Index.