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An optimal bound to access the core in TU-games

By Sylvain Béal, Eric Rémila and Philippe Solal

Abstract

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2.

Topics: C71 - Cooperative Games
Year: 2012
DOI identifier: 10.1007/978-3-642-33996-7_5
OAI identifier: oai:mpra.ub.uni-muenchen.de:38972

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