Algorithmica

, Volume 58, Issue 1, pp 188–220

A Polynomial-Time Algorithm to Find von Neumann-Morgenstern Stable Matchings in Marriage Games

Article

DOI: 10.1007/s00453-010-9388-y

Cite this article as:
Wako, J. Algorithmica (2010) 58: 188. doi:10.1007/s00453-010-9388-y

Abstract

This paper considers von Neumann-Morgenstern (vNM) stable sets in marriage games. Ehlers (Journal of Economic Theory 134: 537–547, 2007) showed that if a vNM stable set exists in a marriage game, the set is a maximal distributive lattice of matchings that includes all core matchings. To determine what matchings form a vNM stable set, we propose a polynomial-time algorithm that finds a man-optimal matching and a woman-optimal matching in a vNM stable set of a given marriage game. This algorithm also generates a modified preference profile such that a vNM stable set is obtained as the core of a marriage game with the modified preference profile. It is well known that cores of marriage games are nonempty. However, the nonemptiness of cores does not imply the existence of a vNM stable set. It is proved using our algorithm that there exists a unique vNM stable set for any marriage game.

Keywords

Matching problem Stable matching von Neumann-Morgenstern stable set 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of EconomicsGakushuin UniversityTokyoJapan

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