A convex representation of totally balanced games
Bilbao, Jesús Mario (Universidad de Sevilla)
Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)

Date:	2012
Abstract:	We analyze the least increment function, a convex function of n variables associated to an n-person cooperative game. Another convex representation of cooperative games, the indirect function, has previously been studied. At every point the least increment function is greater than or equal to the indirect function, and both functions coincide in the case of convex games, but an example shows that they do not necessarily coincide if the game is totally balanced but not convex. We prove that the least increment function of a game contains all the information of the game if and only if the game is totally balanced. We also give necessary and sufficient conditions for a function to be the least increment function of a game as well as an expression for the core of a game in terms of its least increment function.
Grants:	Ministerio de Ciencia e Innovación MTM2008-06695-C03-0 Ministerio de Ciencia e Innovación ECO2010-17766
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Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Subject:	Cooperative games ; Indirect function ; Least increment function
Published in:	Journal of mathematical analysis and applications, Volume 387, Issue 2, (2012) , p. 1167-1175, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2011.10.026

Preprint 12 p, 209.1 KB

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