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Deposit games with reinvestment

Author

Listed:
  • van Gulick, Gerwald
  • Borm, Peter
  • De Waegenaere, Anja
  • Hendrickx, Ruud

Abstract

In a deposit game coalitions are formed by players combining their capital. The proceeds of their investments then have to be divided among those players. The current model extends earlier work on capital deposits by allowing reinvestment of returns. Two specific subclasses of deposit games are introduced. These subclasses provide insight in two extreme cases. It is seen that each term dependent deposit game possesses a core element. Capital dependent deposit games are also shown to have a core element and even a population monotonic allocation scheme if the revenue function exhibits increasing returns to scale. Furthermore, it is shown that all superadditive games are deposit games if one allows for debt.

Suggested Citation

  • van Gulick, Gerwald & Borm, Peter & De Waegenaere, Anja & Hendrickx, Ruud, 2010. "Deposit games with reinvestment," European Journal of Operational Research, Elsevier, vol. 200(3), pages 788-799, February.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:788-799
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    References listed on IDEAS

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    1. Borm, P.E.M. & De Waegenaere, A.M.B. & Rafels, C. & Suijs, J.P.M. & Tijs, S.H. & Timmer, J.B., 1999. "Cooperation in Capital Deposits," Discussion Paper 1999-31, Tilburg University, Center for Economic Research.
    2. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    3. repec:tiu:tiutis:9192543e-378d-4f59-aac6-bbc3200b0dcb is not listed on IDEAS
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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    Cited by:

    1. van Gulick, G. & Norde, H.W., 2011. "Fuzzy Cores and Fuzzy Balancedness," Other publications TiSEM 5792b50b-8b99-46dd-bba5-4, Tilburg University, School of Economics and Management.
    2. Josep Maria Izquierdo & Carlos Rafels, 2020. "Core Allocations in Co-investment Problems," Group Decision and Negotiation, Springer, vol. 29(6), pages 1157-1180, December.
    3. Gerwald Gulick & Henk Norde, 2013. "Fuzzy cores and fuzzy balancedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 131-146, April.

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    More about this item

    Keywords

    Cooperative game theory Deposit games Core elements Population monotonic allocation schemes Superadditive games;

    JEL classification:

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

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