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Stable cores in information graph games

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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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    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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