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

Abstract

AbstractGiven 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.KeywordsEquilibrium PointPolynomial Time AlgorithmEquilibrium OutcomePreference ListStable MarriageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.