Algorithmic Aspects of Equilibria of Stable Marriage Model with Complete Preference Lists

Abstract

Given two sets of agents, men and women, Gale and Shapley discussed a model, called the stable marriage model, in which each agent has a preference over agents of the opposite sex. Gale and Shapley showed that every set of preference lists admits at least one stable marriage by describing an algorithm, called the Gale-Shapley algorithm, which always finds a stable marriage. Given (true) preference lists of men over women and (true) preference lists of women over men, we introduce a game among women. In a play of the game, each woman chooses a strategy which corresponds to a complete preference list over men. The resulting payoff of a woman is her mate determined by men-proposing Gale-Shapley algorithm executed on men’s (true) preference lists and women’s joint strategy. We propose a polynomial time algorithm for checking whether a given marriage is an equilibrium outcome or not.