Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (1): 219-242.doi: 10.1007/s40305-021-00360-x

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Marriage Market with Indifferences: A Linear Programming Approach

Noelia Juarez, Pablo A. Neme, Jorge Oviedo   

  1. Instituto de Matemática Aplicada San Luis, IMASL, RedNIE, Universidad Nacional de San Luis and CONICET, D5700 HHW San Luis, Republica Argentina
  • Received:2019-10-30 Revised:2020-11-26 Online:2023-03-30 Published:2023-02-28
  • Contact: Noelia Juarez, Pablo A. Neme, Jorge Oviedo E-mail:nmjuarez@unsl.edu.ar;paneme@unsl.edu.ar;joviedo@unsl.edu.ar
  • Supported by:
    We acknowledge financial support from UNSL (No. 032016 and 030320), from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)(No. PIP 112-200801-00655), and from Agencia Nacional de Promoción Científica y Tecnológica (No. PICT 2017-2355).

Abstract: We study stable and strongly stable matchings in the marriage market with indifference in their preferences. We characterize the stable matchings as integer extreme points of a convex polytope. We give an alternative proof for the integrity of the strongly stable matching polytope. Also, we compute men-optimal (women-optimal) stable and strongly stable matchings using linear programming. When preferences are strict, we find the men-optimal (women-optimal) stable matching.

Key words: Matching markets, The marriage market with indifferences, Optimal stable matchings, Linear programming

CLC Number: