Matching with Myopic and Farsighted Players

38 Pages Posted: 13 May 2017

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Maastricht University

Ana Mauleon

Université Saint-Louis - Bruxelles; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Vincent Vannetelbosch

Catholic University of Louvain (UCL)

Multiple version iconThere are 2 versions of this paper

Date Written: April 19, 2017

Abstract

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set, which is based on the notion of a myopic-farsighted improving path. A myopic-farsighted stable set is the set of matchings such that there is no myopic-farsighted improving path from any matching in the set to another matching in the set (internal stability) and there is a myopic-farsighted improving path from any matching outside the set to some matching in the set (external stability). For the special cases where all players are myopic and where all players are farsighted, our concept predicts the set of matchings in the core. When all men are myopic and the top choice of each man is a farsighted woman, we show that the singleton consisting of the woman-optimal stable matching is a myopic-farsighted stable set. The same result holds when all women are farsighted. We present examples where this is the unique myopic-farsighted stable set as well as examples of myopic-farsighted stable sets consisting of a core element different from the woman-optimal matching or even of a non-core element.

Keywords: Marriage problems, stable sets, myopic and farsighted players

JEL Classification: C70, C78

Suggested Citation

Herings, P. Jean-Jacques and Mauleon Echeverria, Ana Carmen and Vannetelbosch, Vincent, Matching with Myopic and Farsighted Players (April 19, 2017). Available at SSRN: https://ssrn.com/abstract=2967214 or http://dx.doi.org/10.2139/ssrn.2967214

P. Jean-Jacques Herings (Contact Author)

Maastricht University ( email )

Department of Economics
P.O. Box 616
6200 MD Maastricht
Netherlands
+31 43 3883636 (Phone)
+31 43 3884878 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/p.herings/herings.htm

Ana Carmen Mauleon Echeverria

Université Saint-Louis - Bruxelles ( 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

Vincent Vannetelbosch

Catholic University of Louvain (UCL) ( email )

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

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