On the Gale-Shapley Algorithm for Stable Matchings with a Partial Honesty Nash Refinement

It has long been known that every individually rational matching is obtainable by some Nash equilibrium-even those that make little sense in practice. In the social choice and voting literature, Nash refinements are commonly used to avoid these spurious equilibria. In this paper, we examine the Gale-Shapley algorithm (deferred acceptance) where agents behave strategically but are minimally dishonest, a common refinement in the social choice and voting literature. Under this condition we show that when men propose, every equilibrium corresponds to the woman-optimal marriage, thereby yielding a unique prediction for the outcome for the stable matching problem.