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How to divide a cake when people have different metabolism?

Author

Listed:
  • Luisa Carpente
  • Balbina Casas-Méndez
  • Javier Gozálvez
  • Natividad Llorca
  • Manuel Pulido
  • Joaquín Sánchez-Soriano

Abstract

This paper deals with bankruptcy problems in which the players have different utility functions defined in terms of the quantity of allocated resources. We tackle this kind of situation by means of a game without transferable utility and provide two characterizations of the CEA-rule in this context. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Luisa Carpente & Balbina Casas-Méndez & Javier Gozálvez & Natividad Llorca & Manuel Pulido & Joaquín Sánchez-Soriano, 2013. "How to divide a cake when people have different metabolism?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 361-371, December.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:3:p:361-371
    DOI: 10.1007/s00186-013-0448-3
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Discussion Paper 2000-108, Tilburg University, Center for Economic Research.
    3. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    4. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    5. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    6. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    7. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    8. Joseph Greenberg, 1985. "Cores of Convex Games Without Side Payments," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 523-525, August.
    9. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    10. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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    Cited by:

    1. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    2. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    3. Saavedra-Nieves, Alejandro & Saavedra-Nieves, Paula, 2020. "On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule," European Journal of Operational Research, Elsevier, vol. 285(2), pages 655-669.
    4. Duro Moreno, Juan Antonio & Giménez-Gómez, José Manuel & Sánchez-Soriano, Joaquín & Vilella Bach, Misericòrdia, 2022. "Allocating remaining carbon budgets and mitigation costs," Working Papers 2072/535074, Universitat Rovira i Virgili, Department of Economics.
    5. Gutiérrez, E. & Llorca, N. & Sánchez-Soriano, J. & Mosquera, M., 2018. "Sustainable allocation of greenhouse gas emission permits for firms with Leontief technologies," European Journal of Operational Research, Elsevier, vol. 269(1), pages 5-15.
    6. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.

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