In this paper we explore how the balance of agents on the two sides of a matching market impacts their potential for strategic manipulation. Coles and Shorrer [2014] previously showed that in large, balanced, uniform markets using the Men-Proposing Deferred Acceptance Algorithm, each woman's best response to truthful behavior by all other agents is to truncate her list substantially. In fact, the optimal degree of truncation for such a woman goes to 100% of her list as the market size grows large. Recent findings of Ashlagi et. al. [2014] demonstrate that in unbalanced random markets, the change in expected payoffs is small when one reverses which side of the market ?proposes,? suggesting there is little potential gain from manipulation. Inspired by these findings, we study the implications of imbalance on strategic behavior in the incomplete information setting. We show that the ?long? side has significantly reduced incentives for manipulation in this setting, but that the same doesn't always apply to the ?short? side. We also show that risk aversion and correlation in preferences affect the extent of optimal manipulation.
