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Convexity and marginal contributions in bankruptcy games

Author

Listed:
  • Leobardo Plata-Perez
  • Joss Sanchez-Perez

    () (Universidad Autonoma de San Luis Potosi)

Abstract

En este trabajo analizamos dos definiciones naturales de convexidad para los juegos de bancarrota, una de ellas fue introducida por Aumann y Maschler (1985). En particular, mostramos que la convexidad, entendida como contribuciones marginales crecientes, no se satisface en el juego presentado por estos autores. Ademas proponemos un juego alternativo para capturar situaciones de bancarrota y caracterizamos el antinucleo de este juego; usando la teoria de la dualidad para juegos cooperativos probamos que el nucleo, el antinucleo y el valor de Shapley coinciden con el del juego estudiado por 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 Negocios, 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. 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.
    2. 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.
    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. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bankruptcy problems; cooperative games; convexity; marginal contributions.;

    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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