Axiomatic characterizations of the core without consistency
Sylvain Béal,
Stéphane Gonzalez (),
Philippe Solal and
Peter Sudhölter
Additional contact information
Stéphane Gonzalez: GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique
Working Papers from HAL
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 (search for similar items in EconPapers)
Date: 2022-02
Note: View the original document on HAL open archive server: https://hal.science/hal-04222384v1
References: Add references at CitEc
Citations:
Downloads: (external link)
https://hal.science/hal-04222384v1/document (application/pdf)
Related works:
Journal Article: Axiomatic characterizations of the core without consistency (2023) 
Working Paper: Axiomatic characterizations of the core without consistency (2022) 
Working Paper: Axiomatic characterizations of the core without consistency (2022) 
Working Paper: Axiomatic characterizations of the core without consistency (2022) 
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04222384
Access Statistics for this paper
More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().