期刊名称：Documents de Travail du Centre d'Economie de la Sorbonne
印刷版ISSN：1955-611X
出版年度：2015
出版社：Centre d'Economie de la Sorbonne
摘要：We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and potentials. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, Walsh transform and Fourier analysis etc.). In particular, we present a simple solution to the inverse problem in its general form Given a linear value Φ and a game v , find all games v' such that Φ( v ) = Φ( v' ). Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential.
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