Axiomatic characterizations of the core without consistency

Discussion Papers on Economics, University of Southern Denmark, 2/2022

16 Pages Posted:

See all articles by Peter Sudhölter

Peter Sudhölter

University of Southern Denmark - Department of Business and Economics

Philippe Solal

University of Saint Etienne

Sylvain Béal

affiliation not provided to SSRN

Stéphane Gonzalez

University of Saint Etienne

Date Written: February 17, 2022

Abstract


A TU game is totally positive if it is a linear combination of unanimity games with nonnegative
coefficients. We show that the core on each cone of convex games that contains the
set of totally positive games is characterized by the traditional properties Pareto efficiency,
additivity (ADD), individual rationality, and the null-player property together with one new
property, called unanimity requiring that the solution, when applied to a unanimity game
on an arbitrary coalition, allows to distribute the entire available amount of money to each
player of this coalition. We also show that the foregoing characterization can be generalized
to the domain of balanced games by replacing ADD by "ADD on the set of totally
positive games plus super-additivity (SUPA) in general". Adding converse SUPA allows to
characterize the core on arbitrary domains of TU games that contain the set of all totally
positive games. Converse SUPA requires a vector to be a member of the solution to a game
whenever, when adding a totally positive game such that the sum becomes totally additive,
the sum of the vector and each solution element of the totally positive game belongs to
the solution of the aggregate game. Unlike in traditional characterizations of the core, our
results do not use consistency properties.

Keywords: Core, totally positive games, convex games, super-additivity.

JEL Classification: C71

Suggested Citation

Sudhölter, Peter and Solal, Philippe and Béal, Sylvain and Gonzalez, Stéphane, Axiomatic characterizations of the core without consistency (February 17, 2022). Discussion Papers on Economics, University of Southern Denmark, 2/2022, Available at SSRN: https://ssrn.com/abstract=

Peter Sudhölter (Contact Author)

University of Southern Denmark - Department of Business and Economics ( email )

DK-5230 Odense
Denmark

Philippe Solal

University of Saint Etienne ( email )

6, rue basse des rives
Saint Etienne, 42023
France

Sylvain Béal

affiliation not provided to SSRN

Stéphane Gonzalez

University of Saint Etienne ( email )

6, rue basse des rives
Saint Etienne, 42023
France

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