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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.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 91.

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Length: 18 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:bar:bedcje:200291

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es
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  1. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(3), pages 509-531, September.
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