The Theory of GamesThis book, which first appeared in Chinese, comprises an introduction to game theory. It aims to present the fundamental concepts while developing themes such as continuous games, and n-person non-co-operative and co-operative games in a rigorous fashion. The first part of the book explores the properties of matrix games, and two elementary proofs of the Minimax Theorem are given. The author 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 which is of great significance in this context. Students of mathematics and related subjects will find this to be a readable first account of game theory and an invaluable introduction to key topics. |
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A₁ Assume bimatrix characteristic function choose strategy consider constant-sum continuous function continuous game convex hull defined definition denote dF(x dG(y distribution function domination of imputations elements equation equilibrium point exists expected payoff game is called Hence inequality infinite game kernel least core line segment linear program matrix game max aij max P(x maximum minimax theorem minimum mixed strategy n-person cooperative game n-person non-cooperative game non-empty nucleolus obtain optimal strategy P₁(x P₂(x payoff function payoff matrix payoff to player player 1 receives player 1's player 2 chooses pre-imputations pre-kernel pre-play Proof prove pure strategy r₁ respectively S₁ saddle point satisfies the conditions Shapley value Similarly strategically equivalent strategy of player strategy x strictly convex three-person cooperative game two-person cooperative game undominated v₁ vector vN-M solution x₁ Xe Sm y₁ YESn zero-sum two-person ду