Scandinavian Working Papers in Economics

Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

No 9/2020: Hart-Mas-Colell consistency and the core in convex games

Bas Dietzenbacher () and Peter Sudhölter ()
Additional contact information
Bas Dietzenbacher: Department of Quantitative Economics, Postal: Maastricht University, Maastricht, The Netherlands
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, DK-5230 Odense M, Denmark

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

JEL-codes: C71

17 pages, September 2, 2020

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