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Stable cores in information graph games

Author

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  • Marina Núñez

    (Universitat de Barcelona)

  • Juan Vidal-Puga

    (Universidade de Vigo)

Abstract

In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted.

Suggested Citation

  • Marina Núñez & Juan Vidal-Puga, 2020. "Stable cores in information graph games," UB School of Economics Working Papers 2020/403, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:403web
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    File URL: http://hdl.handle.net/2445/172298
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    References listed on IDEAS

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    1. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    2. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    3. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.
    4. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    5. Joachim Rosenmüller & Benyamin Shitovitz, 2010. "Convex vNM-stable sets for linear production games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 311-318, July.
    6. Jean-Jacques HERINGS & Ana MAULEON & Vincent VANNETELBOSCH, 2017. "Stable sets in matching problems with coalitional sovereignty path dominance," LIDAM Reprints CORE 2861, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Diermeier, Daniel & Fong, Pohan, 2012. "Characterization of the von Neumann–Morgenstern stable set in a non-cooperative model of dynamic policy-making with a persistent agenda setter," Games and Economic Behavior, Elsevier, vol. 76(1), pages 349-353.
    8. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    9. Graziano, Maria Gabriella & Meo, Claudia & Yannelis, Nicholas C., 2017. "Stable sets for exchange economies with interdependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 267-286.
    10. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    11. Einy, Ezra & Shitovitz, Benyamin, 1996. "Convex Games and Stable Sets," Games and Economic Behavior, Elsevier, vol. 16(2), pages 192-201, October.
    12. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
    13. Simon MacKenzie & Manfred Kerber & Colin Rowat, 2015. "Pillage games with multiple stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 993-1013, November.
    14. Hirai, Toshiyuki & Watanabe, Naoki & Muto, Shigeo, 2019. "Farsighted stability in patent licensing: An abstract game approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 141-160.
    15. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    16. Joachim RosenmØller & Benyamin Shitovitz, 2000. "A characterization of vNM-stable sets for linear production games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 39-61.
    17. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    18. Kuipers, Jeroen, 1993. "On the Core of Information Graph Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 339-350.
    19. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2015. "Stable sets for asymmetric information economies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 137-154, March.
    20. Kamal Jain & Rakesh Vohra, 2010. "Extendability and von Neuman–Morgenstern stability of the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 691-697, October.
    21. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 393-401, May.
    22. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
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    Cited by:

    1. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    2. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.

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    More about this item

    Keywords

    Coalitional game; information graph; core; stable set.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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