Multi-sided assignment games on m-partite graphs

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.

Matching markets with middlemen under transferable utility

“…Nevertheless, this property does not extend to the arbitrary multisided markets. Atay and Núñez (2019) recently showed that, in the special case where the market is cycle-free and the valuation function is defined by a specific additivity property, there is for each side an optimal core allocation where all agents of that side achieve their marginal contribution.…”