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Associated consistency, value and graphs

Author

Listed:
  • Gérard Hamiache

    (LEM (UMR CNRS 9221), University of Lille, Domaine Universitaire du Pont de Bois)

  • Florian Navarro

    (LEM (UMR CNRS 9221), University of Lille, Domaine Universitaire du Pont de Bois)

Abstract

This article presents an axiomatic characterization of a new value for cooperative games with incomplete communication. The result is obtained by slight modifications of associated games proposed by Hamiache (Games Econ Behav 26:59–78, 1999; Int J Game Theory 30:279–289, 2001). This new associated game can be expressed as a matrix formula. We generate a series of successive associated games and show that its limit is an inessential game. Three axioms (associated consistency, inessential game, continuity) characterize a unique sharing rule. Combinatorial arguments and matrix tools provide a procedure to compute the solution. The new sharing rule coincides with the Shapley value when the communication is complete.

Suggested Citation

  • Gérard Hamiache & Florian Navarro, 2020. "Associated consistency, value and graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 227-249, March.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:1:d:10.1007_s00182-019-00688-y
    DOI: 10.1007/s00182-019-00688-y
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    References listed on IDEAS

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    1. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    4. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    5. Gérard Hamiache, 2004. "A mean value for games with communication structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 533-544, August.
    6. Gérard Hamiache, 2010. "A Matrix Approach To The Associated Consistency With An Application To The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 175-187.
    7. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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    Cited by:

    1. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Post-Print hal-03678064, HAL.
    2. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    3. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Working Papers hal-03678064, HAL.

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    More about this item

    Keywords

    Cooperative games; Graphs; Associated consistency; Shapley value;
    All these keywords.

    JEL classification:

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

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