Continuous representations of effectivity functions

• Autores: Hans Keiding, Bezalel Peleg
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese, Francisco Ramón Fernández García, 2002, ISBN 84-472-0733-1, pág. 122
• Idioma: inglés
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• Resumen

  • An effectivity function specifies for each coalition a collection of subsets of alternatives such that the coalition can force society�s choice to belong to this subset. Effectivity functions have found widespread application in implementation theory; much recent research is concerned with the so-called representation problem of finding a game form having a prescribed effectivity function.

    In the general setting where the set of alternatives is compact metric space, the problem of finding a continous representation (a representing game form with continuous outcome function) is highly non-trivial. In the present paper we give a new characterization of continuously representable effectivity functions using a property of continuous (not necessarily single valued) selections of certain operations on the subsets selected by the effectivity function.