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On Merge Properties Of The Shapley Value

Author

Listed:
  • JEAN DERKS

    (Department of Mathematics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • STEF TIJS

    (Center and Department of Econometrics, Tilburg University, Tilburg, The Netherlands)

Abstract

Given a transferable utility game, where the players merge into subgroups described by a partition, we address the following question: under which conditions on the characteristic function and partition, merging is beneficial if the Shapley value is applied. Our results can be positioned among the search for well-defined classes of games where merging of players is possible without utility loss in case the Shapley value is chosen as the outcome of the game, and we will report on two of these classes of games arising from telecommunication problems.

Suggested Citation

  • Jean Derks & Stef Tijs, 2000. "On Merge Properties Of The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 249-257.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:04:n:s0219198900000214
    DOI: 10.1142/S0219198900000214
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    Cited by:

    1. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    2. Duygu Yengin, 2012. "Characterizing the Shapley value in fixed-route traveling salesman problems with appointments," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 271-299, May.
    3. Duygu Yengin, 2009. "Appointment Games in Fixed-Route Traveling Salesman Problems and the Shapley Value," School of Economics and Public Policy Working Papers 2009-28, University of Adelaide, School of Economics and Public Policy.
    4. Trine Tornøe Platz & Lars Peter Østerdal, 2013. "Forming and Dissolving Partnerships in Cooperative Game Situations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(2), pages 208-228, April.
    5. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
    6. Ramón Flores & Elisenda Molina & Juan Tejada, 2019. "Evaluating groups with the generalized Shapley value," 4OR, Springer, vol. 17(2), pages 141-172, June.
    7. McQuillin, Ben & Sugden, Robert, 2018. "Balanced externalities and the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 81-92.
    8. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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