Fractional solutions for capacitated NTU-games, with applications to stable matchings

Péter Biró and Tamas Fleiner ()
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Tamas Fleiner: Department of Computer Science and Information Theory Budapest University of Technology and Economics

No 1234, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

Abstract: In this paper we investigate some new 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. Then we describe the interpretation of these results for matching games. Finally we consider an even more general setting where players' contributions in a joint activity may be different. We show that a stable allocation can be found by the Scarf algorithm in this case as well, and we demonstrate the usage of this method for the hospitals resident problem with couples. This problem is relevant in many practical applications, such as NRMP (National Resident Matching Program).

Keywords: Scarf lemma; core; stable matching; stable allocation; hospitals residents problem; couples (search for similar items in EconPapers)
JEL-codes: C61 C71 C78 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2012-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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