The theory of games

Abstract

Part 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.