Abstract
A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.
Highlights
The coalitional game as defined by [1] associates a unique worth with each coalition
In [2]’s definition of a cooperative game, the worth of coalitions depends on the partitions of the rest of society, allowing different worth to be associated with each possible coalition depending on what coalitions are formed in the rest of society (“externalities”)
An membership game (MMG) is a partition function game (PFG) as in [2] if K consists of only one layer
Summary
The coalitional game as defined by [1] associates a unique worth with each coalition. In [2]’s definition of a cooperative game, the worth of coalitions depends on the partitions of the rest of society, allowing different worth to be associated with each possible coalition depending on what coalitions are formed in the rest of society (“externalities”) This representation is still restrictive in the sense that it “presumes that coalitions are mutually exclusive, but in reality, a player might belong to multiple coalitions that interact with one another (e.g., a country might belong to both the United Nations and the European Union)” [3]. Inherent to the model is a new type of “cross externality”: the effect of forming coalitions across spheres Such a formulation is relevant for many applications because, with multiple membership in the underlying application, a compartmentalized approach to the study of each sphere in isolation may lead to wrong conclusions concerning the stability of coalitional agreements.
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