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 n men over n women, and a marriage U, 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 p. 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(2)) time algorithm for finding a set of preference lists, if it exists.
stable marriage gale-shapley algorithm graph theory strategic manipulation