One-to-One Optimal Stable Matchings with Indifferences

 Vade Vate (1989) and Rothblum (1992) characterized the stable matchings of the marriage model with strict preferences as extreme points of a polytope generated by a system of linear inequalities. In this paper, we extend... [ view full abstract ]

 Vade Vate (1989) and Rothblum (1992) characterized the stable matchings of the marriage model with strict preferences as extreme points of a polytope generated by a system of linear inequalities. In this paper, we extend their result by allowing this preferences with indifferences. We characterize stable matchings as integer extreme points of a polytope generated by a new system of linear inequalities. We present a linear integer program that computes a men-optimal (women-optimal) stable matching for the marriage model with indifferences, without artificially breaking the indifferences to strict ordering.