Optimal Sharing Rules in Repeated Partnerships

We study a simple model of repeated partnerships with noisy outcomes. Two partners first choose a sharing rule, under which they start their repeated interaction. We characterize the sharing rule which supports the most efficient equilibrium, and show that it suffices to consider two particular sharing rules. One is an asymmetric sharing rule, which induces only a more productive partner to work. It is optimal for impatient or less productive partners. The other treats them more evenly, and prevails for more productive and patient partners. Those results indicate how technological parameters and patience determine the role of a more productive partner. If the partners become more productive or more patient, the productive partner ceases to be a residual claimant and sacrifices his own share, in order to foster teamwork.