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Abstract:
We generalise the coalition structure core to partition function games. Our definition relies only on one crucial assumption, namely that there is some internal consistency in the game: residuals of the deviation play a game similar to the initial one, and - whenever this is possible - they come to a residual core outcome. Deviating players form their optimistic or pessimistic expectations with this in mind. This leads to a recursive definition of the core. When compared to existing approaches, our core concept has a reduced sensitivity to behavioural assumptions. We look at the core of an economy with a common pool resource defined by Funaki and Yamato (1999) and find that for a number of numerical examples our core concept resolves the puzzle, which arose when more naive approaches were used. We outline possibilities for further extensions.

Core, externalities, partition function, behavioural assumptions, equilibrium binding agreements

Abstract:
We consider partition function games and introduce new definitions of the core that include the effects of externalities. We assume that all players behave rationally and that all stable outcomes arising are consistent with the appropriate generalised concept of the core. The result is a recursive definition of the core where residual subgames are considered as games with fewer players and with a partition function that captures the externalities of the deviating coalition. Some properties of the new concepts are discussed.

partition function form, core

Abstract:
In the model of Funaki and Yamato (IJGT, 1999) the tragedy of the commons can be avoided with pessimistic players, while this does not hold for optimistic players. We propose a new core concept to overcome this puzzle and provide numerical simulations of simple games where the conclusions coincide or are less sensitive to behavioural assumptions.

core, partition function, externalities, behavioural assumptions

Abstract:
For each outcome (i.e. a payoff vector augmented with a coalition structure) of a TU-game with a non-empty coalition structure core there exists a finite sequence of successively dominating outcomes that terminates in the coalition structure core. In order to obtain this result a restrictive dominance relation-which we call enforceable dominance-is employed.

Coalition structure, core-extension, non-emptiness, dominance

Abstract:
Due to the externalities, in normal form games a deviation changes the payoff of all players inducing a retaliation by the remaining or residual players. The stability of an outcome depends on the expectations potential deviators have about this reaction, but so far no satisfactory theory has been provided. The present paper continues the work of Chander and Tulkens (1997) where deviators consider residual equilibria, but we allow coalitions to form, moreover introduce consistency between the residual solution and the solution of the original game. Optimistic and pessimistic considerations produce a pair of cores. These cores are compared to some existing cooperative concepts such as the gamma- and r-cores and the equilibrium binding agreements. In our final section we discuss the predominance of the grand coalition and suggest a generalisation of the normal form where such a precedence can be removed.

externalities, residual game, cohesiveness

Abstract:
This paper strengthens the result of Sengupta and Sengupta (GEB,1996). We show that for the class of TU games with non-empty cores the core can be reached via a bounded number of proposals and counterproposals. Our result is more general than this: the boundedness holds for any two imputations with an indirect dominance relation between them.

dynamic cooperative game, indirect dominance, core

Abstract:
A set of outcomes for a TU-game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core.

Core, Non-emptiness, Indirect Dominance, Outsider Independence

Abstract:
We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced.

The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.

Totally Balanced Games, Exact Games, Convex Games

Abstract:
We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.

Partition Function, Externalities, Implementation, Recursive Core, Stationary Perfect Equilibrium, Time Consistent Equilibrium