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A new order on embedded coalitions: Properties and applications

José Mª Alonso-Meijide (), Mikel Álvarez-Mozos, Gloria Fiestras-Janeiro Mª () and Andrés Jiménez-Losada ()
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José Mª Alonso-Meijide: Universidade de Santiago de Compostela
Gloria Fiestras-Janeiro Mª: Universidade de Vigo
Andrés Jiménez-Losada: Universidad de Sevilla

No 2019/388, UB Economics Working Papers from Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics

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.

Keywords: Partial order; Embedded coalition; Partition function; Convexity. (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2019
New Economics Papers: this item is included in nep-cdm and nep-gth
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