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On existence of equilibrium under social coalition structures

Published online by Cambridge University Press:  29 July 2022

Bugra Caskurlu Open the ORCID record for Bugra Caskurlu [Opens in a new window] ,
Özgün Ekici  and
Fatih Erdem Kizilkaya
Bugra Caskurlu*
Affiliation:
TOBB University of Economics and Technology, Ankara, Turkey
Özgün Ekici
Affiliation:
Ozyegin University, Istanbul, Turkey
Fatih Erdem Kizilkaya
Affiliation:
TOBB University of Economics and Technology, Ankara, Turkey
*
*Corresponding author. Email: bcaskurlu@etu.edu.tr
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Abstract

In a strategic-form game, a strategy profile is an equilibrium if no viable coalition of agents (or players) benefits (in the Pareto sense) from jointly changing their strategies. Weaker or stronger equilibrium notions can be defined by considering various restrictions on coalition formation. For instance, in a Nash equilibrium, it is assumed that viable coalitions are singletons, and in a super strong equilibrium, it is assumed that every coalition is viable. Restrictions on coalition formation can be justified by communication limitations, coordination problems, or institutional constraints. In this paper, inspired by social structures in various real-life scenarios, we introduce certain restrictions on coalition formation, and on their basis, we introduce a number of equilibrium notions. As an application, we study our equilibrium notions in resource selection games (RSGs), and we present a complete set of existence and nonexistence results for general RSGs and their important special cases.

Keywords

Existence of equilibriumresource selection gamescoalition structures
Type
Special Issue: Theory and Applications of Models of Computation (TAMC 2020)
Information
Mathematical Structures in Computer Science , Volume 32 , Issue 2: Theory and Applications of Models of Computation (TAMC 2020) , February 2022 , pp. 216 - 239
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

†

A preliminary version of this paper appeared in the proceedings of the 16th Annual Conference on Theory and Applications of Models of Computation (TAMC 2020).

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