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Reciprocal Equilibria in Link Formation Games

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  • Hannu Salonen

    (University of Turku, Department of Economics, Turku, Finland)

Abstract

We study non-cooperative link formation games in which players have to decide how much to invest in relationships with other players. A link between two players is formed, if and only if both make a positive investment. The cost of forming a link can be interpreted as the value of privacy. We analyze the existence of pure strategy equilibria and the resulting network structures with tractable specifications of utility functions. Sufficient conditions for the existence of reciprocal equilibria are given and the corresponding network structure is analyzed. Pareto optimal and strongly stable network structures are studied. It turns out that such networks are often complete.

Suggested Citation

  • Hannu Salonen, 2015. "Reciprocal Equilibria in Link Formation Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(3), pages 169-183, December.
    • Handle: RePEc:fau:aucocz:au2015_169
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    References listed on IDEAS

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    1. H. Peyton Young & Shmuel Zamir (ed.), 2015. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 4, number 4.
    2. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    5. Sergio Currarini & Matthew O. Jackson & Paolo Pin, 2009. "An Economic Model of Friendship: Homophily, Minorities, and Segregation," Econometrica, Econometric Society, vol. 77(4), pages 1003-1045, July.
    6. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
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    Citations

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    Cited by:

    1. Norma Olaizola & Federico Valenciano, 2020. "Characterization of efficient networks in a generalized connections model with endogenous link strength," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 11(3), pages 341-367, September.
    2. Chiu Ki So, 2016. "Network Formation with Endogenous Link Strength and Decreasing Returns to Investment," Games, MDPI, vol. 7(4), pages 1-9, December.
    3. repec:ehu:ikerla:34463 is not listed on IDEAS
    4. Olaizola, Norma & Valenciano, Federico, 2020. "A connections model with decreasing returns link-formation technology," MPRA Paper 107585, University Library of Munich, Germany.
    5. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    6. Tenev, Anastas P., 2024. "“Friends Are Thieves of Time”: Heuristic attention sharing in stable friendship networks," Journal of Economic Behavior & Organization, Elsevier, vol. 224(C), pages 785-809.
    7. Baumann, Leonie, 2021. "A model of weighted network formation," Theoretical Economics, Econometric Society, vol. 16(1), January.
    8. Fershtman, Chaim & Persitz, Dotan, 2018. "Social Clubs and Social Networks," CEPR Discussion Papers 12874, C.E.P.R. Discussion Papers.
    9. Norma Olaizola & Federico Valenciano, 2023. "A connections model with decreasing returns link-formation technology," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(1), pages 31-61, March.
    10. Walsh, A. M., 2019. "Games on Multi-Layer Networks," Cambridge Working Papers in Economics 1954, Faculty of Economics, University of Cambridge.

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    More about this item

    Keywords

    Link formation games; reciprocal equilibrium; complete network;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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