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Convexity and marginal contributions in bankruptcy games

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  • 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).

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Bibliographic Info

Article provided by Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia. in its journal EconoQuantum, Revista de Economia y Negocios.

Volume (Year): 8 (2011)
Issue (Month): 1 (Julio-Diciembre)
Pages: 61-72

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Handle: RePEc:qua:journl:v:8:y:2011:i:1:p:61-72

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Related research

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

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  1. Robert Aumann, 2010. "Some non-superadditive games, and their Shapley values, in the Talmud," International Journal of Game Theory, Springer, vol. 39(1), pages 3-10, March.
  2. 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.
  3. 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.
  4. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. 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.
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