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On three Shapley-like solutions for cooperative games with random payoffs

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  • Judith Timmer
  • Peter Borm
  • Stef Tijs

Abstract

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided. Copyright Springer-Verlag 2004

Suggested Citation

  • Judith Timmer & Peter Borm & Stef Tijs, 2004. "On three Shapley-like solutions for cooperative games with random payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 595-613, August.
    • Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:595-613
    DOI: 10.1007/s001820400181
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    References listed on IDEAS

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    1. Judith Timmer & Peter Borm & Stef Tijs, 2005. "Convexity In Stochastic Cooperative Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 25-42.
    2. Suijs, J.P.M., 1996. "A Nucleolus for Stochastic Cooperative Games," Other publications TiSEM 44b162e7-85d3-4884-9261-0, Tilburg University, School of Economics and Management.
    3. Suijs, J.P.M., 1996. "A Nucleolus for Stochastic Cooperative Games," Discussion Paper 1996-90, Tilburg University, Center for Economic Research.
    4. K. Ortmann, 1998. "Conservation of energy in value theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 423-449, October.
    5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    6. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
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    Citations

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    Cited by:

    1. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    2. Elena Parilina & Stepan Akimochkin, 2021. "Cooperative Stochastic Games with Mean-Variance Preferences," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    3. Timmer, J.B., 2000. "The Compromise Value for Cooperative Games with Random Payoffs," Discussion Paper 2000-98, Tilburg University, Center for Economic Research.
    4. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    5. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    6. Voorneveld, M. & Grahn, S., 2001. "A Minimal Test for Convex Games and the Shapley Value," Papers 2001:02, Uppsala - Working Paper Series.
    7. S. Alparslan Gök & R. Branzei & S. Tijs, 2010. "The interval Shapley value: an axiomatization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 131-140, June.
    8. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2023. "Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    9. D. Bauso & J. Timmer, 2009. "Robust dynamic cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 23-36, March.
    10. Judith Timmer, 2006. "The Compromise Value for Cooperative Games with Random Payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 95-106, August.
    11. Timmer, J.B., 2000. "The Compromise Value for Cooperative Games with Random Payoffs," Other publications TiSEM 08aefe4e-00a8-4e58-9e54-3, Tilburg University, School of Economics and Management.
    12. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.

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    More about this item

    Keywords

    Cooperative games; Random variables; Shapley value; C71;
    All these keywords.

    JEL classification:

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

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