Scandinavian Working Papers in Economics

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

No 6/2019: Welfare egalitarianism in surplus-sharing problems and convex games

Pedro Calleja (), Francesc Llerena () and Peter Sudhölter ()
Additional contact information
Pedro Calleja: Departament de Matemàtica Econòmica, Postal: Financera i Actuarial, Universitat de Barcelona
Francesc Llerena: Departament de Gestió d’Empreses, Postal: CREIP, Universitat Rovira i Virgili at Reus
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

Abstract: We show that the constrained egalitarian surplus-sharing rule, which divides the surplus so that the poorer players’ resulting payoffs become equal but not larger than any remaining player’s status quo payoff, is characterized by Pareto optimality, path independence, both well-known, and less first (LF), requiring that a player does not gain if her status quo payoff exceeds that of another player by the surplus. This result is used to show that, on the domain of convex games, Dutta-Ray’s egalitarian solution is characterized by aggregate monotonicity (AM), bounded pairwise fairness, resembling LF, and the bilateral reduced game property (2-RGP) à la Davis and Maschler. We show that 2-RGP can be replaced by individual rationality and bilateral consistency à la Hart and Mas-Colell. We prove that the egalitarian solution is the unique core selection that satisfies AM and bounded richness, requiring that the poorest players cannot be made richer within the core. Replacing “poorest” by “poorer” allows to eliminate AM.

Keywords: Surplus-sharing; egalitarianism; convex TU game

JEL-codes: C71

24 pages, March 19, 2019

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