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Title: A new order on embedded coalitions: Properties and Applications
Author: Alonso-Meijide, José Mª
Álvarez-Mozos, Mikel
Fiestras-Janeiro, M. Gloria, 1962-
Jiménez-Losada, Andrés
Keywords: Funcions de variables complexes
Jocs cooperatius (Matemàtica)
Sistemes incrustats (Informàtica)
Particions (Matemàtica)
Functions of complex variables
Embedded computer systems
Cooperative games (Mathematics)
Partitions (Mathematics)
Issue Date: 2019
Publisher: Universitat de Barcelona. Facultat d'Economia i Empresa
Series/Report no: [WP E-Eco19/388]
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.
It is part of: UB Economics – Working Papers, 2019, E18/388
Appears in Collections:UB Economics – Working Papers [ERE]

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