Computing at Glasgow University
Paper ID: 9345
DCS Tech Report Number: TR-2010-315

Fractional solutions for NTU-games
Biro,P. Fleiner,T.

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2010

In this paper we survey some applications of Scarf's Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf's Lemma. Finally, we describe the interpretation of these results for matching games.

Keywords: NTU-game, core, stable matching, stable allocation, Scarf Lemma

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