Scandinavian Working Papers in Economics

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

No 13/2019: Consistency, anonymity, and the core on the domain of convex games

Toru Hokari (), Yukihiko Funaki () and Peter Sudhölter ()
Additional contact information
Toru Hokari: Faculty of Economics, Postal: Keio University
Yukihiko Funaki: School of Political Science and Economics, Postal: Waseda University
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

Abstract: We show that neither Peleg's nor Tadenuma's well-known axiomatizations of the core by non-emptiness, individual rationality, super-additivity, and max consistency or complement consistency, respectively, hold when only convex rather than balanced TU games are considered, even if anonymity is required in addition. Moreover, we show that the core and its relative interior are only two solutions that satisfy Peleg's axioms together with anonymity and converse max consistency on the domain of convex games.

Keywords: Convex TU game; core

JEL-codes: C71

13 pages, December 20, 2019

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