Ata Atay

interaction seminar

Ata Atay

Hungarian Academy of Sciences
Multi-sided assignment games on m-partite graphs
Venue

IBD Salle 16

Îlot Bernard du Bois - Salle 16

AMU - AMSE
5-9 boulevard Maurice Bourdet
13001 Marseille

Date(s)
Thursday, March 21 2019| 12:00pm to 1:15pm
Contact(s)

Mathieu Faure: mathieu.faure[at]univ-amu.fr
Gaëtan Fournier: gaetan.fournier[at]univ-amu.fr

Abstract

We consider a multi-sided assignment game with the following characteristics: (a) the agents are organized in m sectors that are connected by a graph that induces a weighted m-partite graph on the set of agents, (b) a basic coalition is formed by agents from different connected sectors, and (c) the worth of a basic coalition is the addition of the weights of all its pairs that belong to connected sectors. We provide a sufficient condition on the weights to guarantee balancedness of the related multi-sided assignment game. Moreover, when the graph on the sectors is cycle-free, we prove the game is strongly balanced and the core is fully described by means of the cores of the underlying two-sided assignment games associated with the edges of this graph. As a consequence, the complexity of the computation of an optimal matching is reduced and existence of optimal core allocations for each sector of the market is guaranteed.

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