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Multi-sided assignment games on m-partite graphs
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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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ATAY, Ata i NÚÑEZ, Marina (Núñez Oliva). Multi-sided assignment games on m-partite graphs. Annals of Operations Research. 2019. Vol. 279, núm. 1-2, pàgs. 271-290. ISSN 0254-5330. [consulta: 8 de maig de 2026]. Disponible a: https://hdl.handle.net/2445/150702