Multi-sided assignment games on m-partite graphs

Ata Atay and Marina Núñez ()

Annals of Operations Research, 2019, vol. 279, issue 1, No 10, 290 pages

Abstract: 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.

Keywords: Cooperative games; Multi-sided assignment games; Core; 91A12; 91A43 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10479-019-03256-5

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