《《coal》.pdf

GAME THEORY Thomas S. Ferguson Part IV. Games in Coalitional Form 1. Many-Person TU Games. 1.1 Coalitional Form. Characteristic Functions. 1.2 Relation to Strategic Form. 1.3 Constant-Sum Games. 1.4 Example. 1.5 Exercises. 2. Imputations and the Core. 2.1 Imputations. 2.2 Essential Games. 2.3 The Core. 2.4 Examples. 2.5 Exercises. 3. The Shapley Value. 3.1 Value Functions. The Shapley Axioms. 3.2 Computation of the Shapley Value. 3.3 An Alternative Form of the Shapley Value. 3.4 Simple Games. The Shapley-Shubik Power Index. 3.5 Exercises. 4. The Nucleolus. 4.1 Definition of the Nucleolus. 4.2 Properties of the Nucleolus. 4.3 Computation of the Nucleolus. 4.4 Exercises. IV – 1 PART IV. Games in Coalitional Form 1. Many-Person TU Games We now consider many-person cooperative games. In such games there are no restrictions on the agreements that may be reached among the players. In addition, we assume that all payoffs are measured in the same units and that there is a transferrable utility which allows side payments to be made among the players. Side payments may be used as inducements for some players to use certain mutually beneficial strategies. Thus, there will be a tendency for players, whose objectives in the game are close, to form alliances or coalitions. The structure given to the game by coalition formation is conveniently studied by reducing the game to a form in which coalitions play a central role. After defining the coalitional form of a many-person TU game, we shall learn how to transform games from strategic form to coalitional form and vice versa.