The Maximal Payoff and Coalition Formation in Coalitional Games *
نویسنده
چکیده
This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then provides answers to the questions of what payoffs to split, how to split the payoff, what coalitions to form, and how long each of the coalitions will be formed by rational players in coalitional TU games. Finally, it obtains analogous results in coalitional NTU (non-transferable utility) games.
منابع مشابه
Coalition-Proof Nash Equilibria and the Core in Three-Player Games
We study 3-person noncooperative games of coalition formation where the underlying situation is represented by a game in coalitional form without side payments. We look at coalition-proof Nash equilibria and we show that if the underlying game is balanced (in the sense of Scarf), then, except for indifferences, the grand coalition forms, and the payoff is in the core. If the underlying game has...
متن کاملSequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division
This paper analyzes a sequential game of coalition formation when the division of the coalitional surplus is fixed and the payoffs are defined relative to the whole coalition structure. Gains from cooperation are represented by a valuation which maps coalition structures into payoff vectors. I show that any core stable coalition structure can be attained as a stationary perfect equilibrium of t...
متن کاملEcon 618: Topic 11 Introduction to Coalitional Games
Consider a game with a finite set of players. A coalition is a nonempty subset of the set of players. A coalitional game with transferable payoff consists of (1) a finite set of players, N (2) a function v : S ⊆ N −→ R. The value of the function for a given S, v(S) is known as the worth of the coalition S. v(S) is the total payoff that is available for division among the members of the coalitio...
متن کاملStationary Consistent Equilibrium Coalition Structures Constitute the Recursive Core
We study coalitional games where the coalitional payoffs depend on the entire coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursive-balanced partition function form games we in...
متن کاملComputing Shapley Value in Supermodular Coalitional Games
Coalitional games allow subsets (coalitions) of players to cooperate to receive a collective payoff. This payoff is then distributed “fairly” among the members of that coalition according to some division scheme. Various solution concepts have been proposed as reasonable schemes for generating fair allocations. The Shapley value is one classic solution concept: player i’s share is precisely equ...
متن کامل