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Convexity and marginal contributions in bankruptcy games

Author

Listed:
  • Leobardo Plata-Perez

    (Universidad Autonoma de San Luis Potosi)

  • Joss Sanchez-Perez

    (Universidad Autonoma de San Luis Potosi)

Abstract

In this paper we analyze two natural convexity definitions for cooperative bankruptcy games, one of them was introduced by Aumann and Maschler (1985). In particular, we show that convexity in the sense of increasing marginal contributions is not satisfied by the game introduced by these authors. Furthermore, we propose an alternative game that captures the situation of bankruptcy problems and characterize the anticore of such game; and using duality theory of cooperative games, we show that the core, anticore and its Shapley value coincide with the one studied by Aumann and Maschler (1985).

Suggested Citation

  • Leobardo Plata-Perez & Joss Sanchez-Perez, 2011. "Convexity and marginal contributions in bankruptcy games," EconoQuantum, Revista de Economia y Finanzas, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 8(1), pages 61-72, Julio-Dic.
    • Handle: RePEc:qua:journl:v:8:y:2011:i:1:p:61-72
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    5. Robert Aumann, 2010. "Some non-superadditive games, and their Shapley values, in the Talmud," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 3-10, March.
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    More about this item

    Keywords

    Bankruptcy problems; cooperative games; convexity; marginal contributions.;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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