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The Compromise Value for Cooperative Games with Random Payoffs

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  • Judith Timmer

Abstract

This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:1:p:95-106
    DOI: 10.1007/s00186-006-0072-6
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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. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    3. 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.
    4. Stef Tijs & Gert-Jan Otten, 1993. "Compromise values in cooperative game theory," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 1-36, December.
    5. Tijs, S.H. & Otten, G.J.M., 1993. "Compromise values in cooperative game theory," Research Memorandum FEW 615, Tilburg University, School of Economics and Management.
    6. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    7. Tijs, S.H. & Otten, G.J.M., 1993. "Compromise values in cooperative game theory," Other publications TiSEM 0f7c6f08-1cec-4b83-942a-5, Tilburg University, School of Economics and Management.
    8. Tijs, S.H. & Otten, G.J.M., 1993. "Compromise values in cooperative game theory," Other publications TiSEM 59116a16-eeef-4571-9c8d-b, Tilburg University, School of Economics and Management.
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    Cited by:

    1. 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.
    2. 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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