## 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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### Contents

MATRIX GAMES | 1 |

CONTINUOUS GAMES | 41 |

NPERSON NONCOOPERATIVE GAMES | 75 |

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### Common terms and phrases

Axiom bimatrix characteristic function choose strategy coalition 1,2 coalition structure consider continuous function continuous game convex hull core C(T defined definition denote dF(x distribution function domination of imputations element equation equilibrium point exists expected payoff game is called grand coalition Hence imputation triangle inequality infinite game least core Lemma Let the payoff lexicographic centre line segment linear program matrix game max min P(x max P(x minimax theorem minimum mixed strategy n-person cooperative game n-person non-cooperative game non-empty nucleolus obtain optimal strategy payoff function payoff matrix payoff to player player 1 chooses player 1 receives player l's pre-imputations pre-kernel pre-play Proof prove pure strategy region respectively saddle point satisfies the conditions Shapley value side Similarly strategically equivalent strategy of player strategy X strictly convex strong e-core subsets Suppose three-person cooperative game two-person cooperative game undominated vector vN-M solution XAYt XeSm zero-sum two-person