Properties of Solutions for Games on Union-Closed Systems

Rene van den Brink; Ilya Katsev; Gerard van der Laan

doi:10.3390/math11040980

Properties of Solutions for Games on Union-Closed Systems

Rene van den Brink^*
, Ilya Katsev
, Gerard van der Laan

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature, various models of games with restricted cooperation can be found where, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider games on a union-closed system where the set of feasible coalitions is closed under the union, i.e., for any two feasible coalitions also, their union is feasible. Properties of solutions (the core, the nucleolus, and the prekernel) are discussed for games on a union-closed system.

Original language	English
Article number	980
Pages (from-to)	1-16
Number of pages	16
Journal	Mathematics
Volume	11
Issue number	4
DOIs	https://doi.org/10.3390/math11040980
Publication status	Published - 2 Feb 2023

Bibliographical note

This article belongs to the Special Issue: Trends in Game Theory and Its Applications.

Publshed online: 14-02-2023

Publisher Copyright:
© 2023 by the authors.

Funding

This research was funded by Dutch Research Council, NWO-grant 047.017.017.

Funders	Funder number
NWO-Grant
???publication-publication-funding-organisation-not-added???	047.017.017

Keywords

core
nucleolus
prekernel
restricted cooperation
TU-game
union-closed system

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10.3390/math11040980

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Properties of Solutions for Games on Union-Closed Systems

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