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 Kóczy [7], Yang [13, 14] and a previous result by ourselves [2] in which the bound was n(n − 1)/2.
Financial support by the National Agency for Research (ANR) — research programs “Models of Influence and Network Theory” (MINT) ANR.09.BLANC-0321.03 and “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) — and by IXXI (Complex System Institute, Lyon) is gratefully acknowledged.
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Béal, S., Rémila, E., Solal, P. (2012). An Optimal Bound to Access the Core in TU-Games. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_5
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