We study whether people's behavior in unbalanced gift exchange markets with repeated interaction are affected by whether they are on the excess supply side or the excess demand side of the market. Our analysis is based on the comparison of behavior between two types of experimental gift exchange markets, which vary only with respect to whether first or second movers are on the long side of the market. The direction of market imbalance could influence subjects' behavior, as second movers (workers) might react differently to favorable actions by first movers (firms) in the two cases. While our data show strong deviations from the standard game-theoretic prediction, we find mainly secondary treatment effects. Wage offers are not higher when there is an excess supply of firms, and workers do not respond more favorably to a given wage when there is an excess supply of labor. The state of competition does not appear to have strong effects in our data. We also present data from single-period sessions that show substantial gift exchange even without repeated interactions.