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.
Original language | English |
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Pages (from-to) | 413-429 |
Number of pages | 17 |
Journal | International Journal of Game Theory |
Volume | 51 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2022 |
JEL classifications
- c71 - Cooperative Games
Keywords
- Shapley value
- consistency
- converse consistency
- convex games
- core
- Convex games
- REDUCED GAME
- AXIOMATIZATION
- Consistency
- Converse consistency
- Core