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Multi-sided assignment games on m-partite graphs

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  • Ata Atay

    (Hungarian Academy of Sciences)

  • Marina Núñez

    (University of Barcelona)

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.

Suggested Citation

  • Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    • Handle: RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-019-03256-5
    DOI: 10.1007/s10479-019-03256-5
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    Cited by:

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    More about this item

    Keywords

    Cooperative games; Multi-sided assignment games; Core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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