Dominance Invariant Roommate Problems

22 Pages Posted: 16 Jun 2012

See all articles by Ana Mauleon

Ana Mauleon

Catholic University of Louvain (UCL)

Elena Molis

affiliation not provided to SSRN

Vincent J. Vannetelbosch

Center for Operations Research and Econometrics (CORE)

Wouter Vergote

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Facultés Universitaires Saint Louis à Bruxelles - CEREC

Date Written: January 4, 2012

Abstract

Solution concepts in social environments use either a direct or indirect dominance relationship, depending on whether it is assumed that agents are myopic or farsighted. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (indirect) agents could be very different. In this paper, we characterize dominance invariant roommate problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in roommate problems and give these an intuitive interpretation. Whenever some of the conditions are not satisfied, it is important to know the kind of agents that are being investigated in order to use the appropriate stability concept. Furthermore, we characterize dominance invariant roommate problems having a non-empty core. Finally, we show that, if the core of a dominance invariant roommate problem is not empty, it contains a unique matching, the dominance invariant stable matching, in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.

Keywords: roommate problems, direct dominance, indirect dominance

JEL Classification: C71, C78

Suggested Citation

Mauleon, Ana and Molis, Elena and Vannetelbosch, Vincent J. and Vergote, Wouter and Vergote, Wouter, Dominance Invariant Roommate Problems (January 4, 2012). Available at SSRN: https://ssrn.com/abstract=1984892 or http://dx.doi.org/10.2139/ssrn.1984892

Ana Mauleon

Catholic University of Louvain (UCL)

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium

Elena Molis (Contact Author)

affiliation not provided to SSRN ( email )

Vincent J. Vannetelbosch

Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
1348 Louvain-la-Neuve, 1348
Belgium

Wouter Vergote

Facultés Universitaires Saint Louis à Bruxelles - CEREC ( email )

Brussels, 1000
Belgium

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

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