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A Note on Shapleys Convex Measure Games

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  • Fco. Javier Martinez de Albeniz Salas
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

L. S. Shapley, in his paper Cores of Convex Games, introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players.

Suggested Citation

  • Fco. Javier Martinez de Albeniz Salas & Carlos Rafels Pallarola, 2002. "A Note on Shapleys Convex Measure Games," Working Papers in Economics 91, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:200291
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    References listed on IDEAS

    as
    1. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    2. Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
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    JEL classification:

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

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