A New Order on Embedded Coalitions: Properties and Applications

UB Economics Working Papers E19/388

30 Pages Posted: 2 May 2019

See all articles by José María Alonso-Meijide

José María Alonso-Meijide

Universidade de Santiago de Compostela

Mikel Alvarez-Mozos

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics

M. Gloria Fiestras-Janeiro

University of Vigo

Andres Jimenez-Losada

University of Seville

Date Written: March 28, 2019

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

JEL Classification: C71

Suggested Citation

Alonso-Meijide, José María and Alvarez-Mozos, Mikel and Fiestras-Janeiro, M. Gloria and Jimenez-Losada, Andres, A New Order on Embedded Coalitions: Properties and Applications (March 28, 2019). UB Economics Working Papers E19/388, Available at SSRN: https://ssrn.com/abstract=3363587 or http://dx.doi.org/10.2139/ssrn.3363587

José María Alonso-Meijide (Contact Author)

Universidade de Santiago de Compostela ( email )

Complejo Docente - Campus Universitario de Lugo
Lugo, A Coruña 15704
Spain

Mikel Alvarez-Mozos

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics ( email )

Avda. Diagonal 690
Barcelona, 08034
Spain

M. Gloria Fiestras-Janeiro

University of Vigo ( email )

Campus Universitario Lagoas-Marcosende
Vigo, 36200
Spain

Andres Jimenez-Losada

University of Seville

Sevilla
Spain

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