Hart–Mas-Colell consistency and the core in convex games

Bas Dietzenbacher and Peter Sudhölter

International Journal of Game Theory, 2022, vol. 51, issue 2, No 7, 413-429

Abstract: 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.

Keywords: Convex games; Consistency; Converse consistency; Core; Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Working Paper: Hart-Mas-Colell consistency and the core in convex games (2020)
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DOI: 10.1007/s00182-021-00798-6

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