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
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
We show that the core on the domain of convex games is axiomatized by efficiency, unanimity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency
Summary
Interactive situations where players are able to generate revenues in coalitions can be modeled as cooperative games with transferable utility. In this model, the worth of each coalition represents the monetary opportunities when these players join forces. Once the grand coalition is formed, the worths of subcoalitions serve as benchmarks for a fair allocation of the worth of the grand coalition. Solutions assign to each transferable utility game a set of recommended allocations for the cooperating players. These solutions are fundamentally distinguished on the basis of axioms, i.e., formal expressions of properties which may or may not be satisfied
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