<XML><RECORDS><RECORD><REFERENCE_TYPE>10</REFERENCE_TYPE><REFNUM>9345</REFNUM><AUTHORS><AUTHOR>Biro,P.</AUTHOR><AUTHOR>Fleiner,T.</AUTHOR></AUTHORS><YEAR>2010</YEAR><TITLE>Fractional solutions for NTU-games</TITLE><PLACE_PUBLISHED>DCS Technical Report Series</PLACE_PUBLISHED><PUBLISHER>Dept of Computing Science, University of Glasgow</PUBLISHER><ISBN>TR-2010-315</ISBN><LABEL>Biro:2010:9345</LABEL><KEYWORDS><KEYWORD>NTU-game</KEYWORD></KEYWORDS<ABSTRACT>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.</ABSTRACT></RECORD></RECORDS></XML>