Asymptotic Values of Vector Measure Games
AbstractThe asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ?(S) where ? is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where a two-house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games. All weighted majority games have an asymptotic value. However, not all two-house weighted majority games have an asymptotic value. In this paper we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two-house weighted majority games.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp344.
Length: 60 pages
Date of creation: Nov 2003
Date of revision:
Publication status: Forthcoming in Mathematics of Operations Research
asymptotic value; weighted majority game; two-house weighted; majority game; vector measure game; Shapley value;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-11-23 (All new papers)
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