Successful Manipulation in Stable Marriage Model with Complete Preference Lists

This paper deals with a strategic issue in the stable marriage model with complete preference lists (i.e., a preference list of an agent is a permutation of all the members of the opposite sex). Given complete preference lists of nmen over n women, and a marriage μ, we consider the problem for finding preference lists of n women over n men such that the men-proposing deferred acceptance algorithm (Gale-Shapley algorithm) adopted to the lists produces μ. We show a simple necessary and sufficient condition for the existence of a set of preference lists of women over men. Our condition directly gives an O(n) time algorithm for finding a set of preference lists, if it exists.