A Note on Shapleys Convex Measure Games
AbstractL. 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 InfoPaper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 91.
Length: 18 pages
Date of creation: 2002
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Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- 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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