Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-16T11:26:43.493Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).

References

Anshelevich, E., Caskurlu, B. and Hate, A. (2013). Partition equilibrium always exists in resource selection games. Theory of Computing Systems 53 (1) 73–85.CrossRefGoogle Scholar
Ashlagi, I., Krysta, P. and Tennenholtz, M. (2008). Social context games. In: International Workshop on Internet and Network Economics, Berlin, Heidelberg, Springer.Google Scholar
Aumann, R. J. (1959). Acceptable points in general cooperative n-person games. Contributions to the Theory of Games 4 287–324.Google Scholar
Baye, M. R., Tian, G. and Zhou, J. (1993). Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs. The Review of Economic Studies 60 (4) 935–948.CrossRefGoogle Scholar
Bernheim, B. D., Peleg, B. and Whinston, M. D. (1987). Coalition-proof Nash equilibria concepts. Journal of Economic Theory 42 (1) 1–12.CrossRefGoogle Scholar
Caskurlu, B., Ekici, Ö. and Kizilkaya, F. E. (2020). On efficient computation of equilibrium under social coalition structures. Turkish Journal of Electrical Engineering & Computer Sciences 28 (3) 1686–1698.CrossRefGoogle Scholar
Caskurlu, B., Ekici, Ö. and Kizilkaya, F. E. (2021). On singleton congestion games with resilience against collusion. In: The 27th International Computing and Combinatorics Conference (COCOON).Google Scholar
Feldman, M. and Tennenholtz, M. (2010). Structured coalitions in resource selection games. ACM Transactions on Intelligent Systems and Technology 1 (1) 1–21.CrossRefGoogle Scholar
Hayrapetyan, A., Tardos, É. and Wexler, T. (2006). The effect of collusion in congestion games. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC), 89–98.CrossRefGoogle Scholar
Hoefer, M., Penn, M., Polukarov, M., Skopalik, A. and Vöcking, B. (2011). Considerate equilibrium. In: International Joint Conference on Artificial Intelligence (IJCAI).Google Scholar
Holzman, R. and Law-Yone, N. (1997). Strong equilibrium in congestion games. Games and Economic Behavior 21 (1–2) 85–101.CrossRefGoogle Scholar
Konishi, H., Le Breton, M. and Weber, S. (1997). Equilibria in a model with partial rivalry. Journal of Economic Theory 72 (1) 225–237.CrossRefGoogle Scholar
Konishi, H., Le Breton, M. and Weber, S. (1999). On coalition-proof Nash equilibria in common agency games. Journal of Economic Theory 85 (1) 122–139.CrossRefGoogle Scholar
Kuniavsky, S. and Smorodinsky, R. (2014). Equilibrium and potential in coalitional congestion games. Theory and Decision 76 (1) 69–79.CrossRefGoogle Scholar
Milchtaich, I. (1996). Congestion games with player-specific payoff functions. Games and Economic Behavior 13 (1) 111–124.CrossRefGoogle Scholar
Milinski, M. (1979). An evolutionarily stable feeding strategy in sticklebacks. Zeitschrift für Tierpsychologie 51 (1) 36–40.CrossRefGoogle Scholar
Monderer, D. and Shapley, L. S. (1996). Potential games. Games and Economic Behavior 14 (1) 124–143.CrossRefGoogle Scholar
Moreno, D. and Wooders, J. (1996). Coalition-proof equilibrium. Games and Economic Behavior 17 (1) 80–112.CrossRefGoogle Scholar
Nash, J. (1951). Non-cooperative games. Annals of Mathematics 54 (2) 286–295.CrossRefGoogle Scholar
Quint, T. and Shubik, M. (1994). A model of migration. Cowles Foundation for Research in Economics, 1088.Google Scholar
Reny, P. J. (1999). On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67 (5) 1029–1056.CrossRefGoogle Scholar
Rosenthal, R. W. (1971). A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2 (1) 65–67.CrossRefGoogle Scholar