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A new order on embedded coalitions: Properties and applications

Author

Listed:
  • José Mª Alonso-Meijide

    (Universidade de Santiago de Compostela)

  • Mikel Álvarez-Mozos

    (Universitat de Barcelona)

  • Mª Gloria Fiestras-Janeiro

    (Universidade de Vigo)

  • Andrés Jiménez-Losada

    (Universidad de Sevilla)

Abstract

Given a finite set of agents, an embedded coalition consists of a coalition and a partition of the rest of agents. We study a partial order on the set of embedded coalitions of a finite set of agents. An embedded coalition precedes another one if the first coalition is contained in the second and the second partition equals the first one after removing the agents in the second coalition. This poset is not a lattice. We describe the maximal lower bounds and minimal upper bounds of a finite subset, whenever they exist. It is a graded poset and we are able to count the number of elements at a given level as well as the total number of chains. The study of this structure allows us to derive results for games with externalities. In particular, we introduce a new concept of convexity and show that it is equivalent to having non-decreasing contributions to embedded coalitions of increasing size.

Suggested Citation

  • José Mª Alonso-Meijide & Mikel Álvarez-Mozos & Mª Gloria Fiestras-Janeiro & Andrés Jiménez-Losada, 2019. "A new order on embedded coalitions: Properties and applications," UB School of Economics Working Papers 2019/388, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:388web
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    File URL: http://hdl.handle.net/2445/131210
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    Cited by:

    1. Frank Huettner & André Casajus, 2019. "Marginality, dividends, and the value in games with externalities," ESMT Research Working Papers ESMT-19-01, ESMT European School of Management and Technology.

    More about this item

    Keywords

    Partial order; Embedded coalition; Partition function; Convexity.;
    All these keywords.

    JEL classification:

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

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