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Friends and enemies: a model of signed network formation

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  • Hiller, Timo

    (Department of Economics, University of Bristol)

Abstract

I propose a simple model of signed network formation, where agents make friends to extract payoffs from weaker enemies. The model thereby accounts for the interplay between friendship and alliance on one hand and enmity and antagonism on the other. Nash equilibrium configurations are such that, either everyone is friends with everyone, or agents can be partitioned into different sets, where agents within the same set are friends and agents in different sets are enemies. Any strong Nash equilibrium must be such that a single agent is in an antagonistic relationship with everyone else. Furthermore, we show that Nash equilibria cannot be Pareto ranked. This paper offers a game-theoretic foundation for a large body of work on signed networks, called structural balance theory, which has been studied in sociology, social psychology, bullying, international relations and applied physics. The paper also contributes to the literature on contests and economics of conflict.

Suggested Citation

  • Hiller, Timo, 2017. "Friends and enemies: a model of signed network formation," Theoretical Economics, Econometric Society, vol. 12(3), September.
    • Handle: RePEc:the:publsh:1937
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    References listed on IDEAS

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    Cited by:

    1. Kenan Huremović, 2021. "A noncooperative model of contest network formation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 275-317, April.
    2. Zenou, Yves & Xu, Jin & Zhou, Junjie, 2019. "Networks in Conflict: A Variational Inequality Approach," CEPR Discussion Papers 13647, C.E.P.R. Discussion Papers.
    3. Erol, Selman & Vohra, Rakesh, 2022. "Relationship externalities," Journal of Economic Theory, Elsevier, vol. 206(C).
    4. Dziubiński, Marcin & Goyal, Sanjeev & Minarsch, David E.N., 2021. "The strategy of conquest," Journal of Economic Theory, Elsevier, vol. 191(C).
    5. Bozbay, Irem & Vesperoni, Alberto, 2018. "A contest success function for networks," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 404-422.
    6. Zenou, Yves & Amarasinghe, Ashani & Raschky, Paul & Zhou, Junjie, 2020. "Conflicts in Spatial Networks," CEPR Discussion Papers 14300, C.E.P.R. Discussion Papers.
    7. Dongryul Lee & Pilwon Kim, 2022. "Group formation in a dominance-seeking contest," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 39-68, January.
    8. Sun, Xiang & Xu, Jin & Zhou, Junjie, 2023. "Effort discrimination and curvature of contest technology in conflict networks," Games and Economic Behavior, Elsevier, vol. 142(C), pages 978-991.
    9. Hajdu Tamás & Kertesi Gábor & Kézdi Gábor, 2019. "Inter-Ethnic Friendship and Hostility between Roma and non-Roma Students in Hungary: The Role of Exposure and Academic Achievement," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 19(1), pages 1-17, January.
    10. Michael D. König & Dominic Rohner & Mathias Thoenig & Fabrizio Zilibotti, 2017. "Networks in Conflict: Theory and Evidence From the Great War of Africa," Econometrica, Econometric Society, vol. 85, pages 1093-1132, July.
    11. Pandey, Siddhi Gyan, 2021. "A model of signed network formation with heterogeneous players," Research in Economics, Elsevier, vol. 75(1), pages 119-128.
    12. Cai, Xinyue & Kimya, Mert, 2023. "Stability of alliance networks," Games and Economic Behavior, Elsevier, vol. 140(C), pages 401-409.
    13. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2022. "Equilibrium characterization and shock propagation in conflict networks," Journal of Economic Theory, Elsevier, vol. 206(C).
    14. Luke A. Boosey & Christopher Brown, 2021. "Contests with Network Externalities: Theory & Evidence," Working Papers wp2021_07_02, Department of Economics, Florida State University.
    15. Hideto Koizumi, 2023. "Escalation of a local conflict into a Cold War," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-6, December.
    16. Serhat Doğan & Kerim Keskin & Çağrı Sağlam, 2020. "Contests over joint production on networks," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(2), pages 377-400, April.
    17. Kris De Jaegher, 2021. "Common‐Enemy Effects: Multidisciplinary Antecedents And Economic Perspectives," Journal of Economic Surveys, Wiley Blackwell, vol. 35(1), pages 3-33, February.
    18. Peter-J. Jost, 2021. "Endogenous formation of entrepreneurial networks," Small Business Economics, Springer, vol. 56(1), pages 39-64, January.
    19. Zenou, Yves & Bochet, Olivier & Faure, Mathieu & Long, Yan, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    20. Pedro Cisneros-Velarde & Francesco Bullo, 2020. "Signed Network Formation Games and Clustering Balance," Dynamic Games and Applications, Springer, vol. 10(4), pages 783-797, December.
    21. Bettina Klaus & Flip Klijn & Seçkin Özbilen, 2023. "Core Stability and Strategy-Proofness in Hedonic Coalition Formation Problems with Friend-Oriented Preferences," Working Papers 1399, Barcelona School of Economics.
    22. Bochet, Olivier & Faure, Mathieu & Long, Yan & Zenou, Yves, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    23. Cortes-Corrales, Sebastián & Gorny, Paul M., 2018. "Generalising Conflict Networks," MPRA Paper 90001, University Library of Munich, Germany.

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    More about this item

    Keywords

    Signed network formation; structural balance; contest success function; bullying; economics of conflict; international relations;
    All these keywords.

    JEL classification:

    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • F51 - International Economics - - International Relations, National Security, and International Political Economy - - - International Conflicts; Negotiations; Sanctions

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