We devise an experiment to explore the effect of different degrees of bargaining power on the design and the selection of contracts in a hidden-information context. In our benchmark case, each principal is matched with one agent of unknown type. In our second treatment, a principal can select one of three agents, while in a third treatment an agent may choose between the contract menus offered by two principals. We first show theoretically how different ratios of principals and agents affect outcomes and efficiency. Informational asymmetries generate inefficiency. In an environment where principals compete against each other to hire agents, these inefficiencies may disappear, but they are insensitive to the number of principals. In contrast, when agents compete to be hired, efficiency improves dramatically, and it increases in the relative number of agents because competition reduces the agents' informational monopoly power. However, this environment also generates a high inequality level and is characterized by multiple equilibria. In general, there is a fairly high degree of correspondence between the theoretical predictions and the contract menus actually chosen in each treatment. There is, however, a tendency to choose more 'generous' (and more efficient) contract menus over time. We find that competition leads to a substantially higher probability of trade, and that, overall, competition between agents generates the most efficient outcomes.