Abstract
This paper formally introduces Hart-Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart-Mas-Colell consistency, and converse Hart-Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.
Highlights
Interactive situations where players are able to generate revenues in coalitions can be modeled as cooperative games with transferable utility
Inspired by Davis and Maschler (1965), Peleg (1986) showed that the core is consistent when the worth of a coalition of remaining players in reduced games is defined as the maximal surplus to any subgroup of leaving players, and that this reduced game property characterizes the core in conjunction with individual rationality and superadditivity
We show that the core is the unique inclusion-wise maximal solution satisfying individual rationality and a weak version of Hart-Mas-Colell consistency on the domain of convex games and we derive a pure axiomatic characterization
Summary
Interactive situations where players are able to generate revenues in coalitions can be modeled as cooperative games with transferable utility. Inspired by Davis and Maschler (1965), Peleg (1986) showed that the core is consistent when the worth of a coalition of remaining players in reduced games is defined as the maximal surplus to any subgroup of leaving players, and that this reduced game property characterizes the core in conjunction with individual rationality and superadditivity. Tadenuma (1992) showed that the core is consistent when the worth of a coalition of remaining players in reduced games is defined as the surplus to all leaving players, and that this reduced game property characterizes the core in conjunction with individual rationality. The relation of the core with another well-known consistency axiom formulated by Hart and Mas-Colell (1989) has not been studied so far This reduced game property was originally introduced for single-valued solutions and explored for the Shapley value (Shapley 1953).
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