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 partnerships with patient partners. Those results indicate that the role of a more productive partner crucially depends on technological parameters and patience. 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. JEL Classification Numbers: C72, C73, L23, P13. ∗This project started when Ohta was a research fellow under the 21st Century COE Research Program at Kyoto University. Ohta and Sekiguchi thank the Program for support. We are grateful to audience at Yokohama National University, Hitotsubashi University, Shanghai Jiao Tong University, Otaru University of Commerce, Yonsei University, SWET 2007, the 13th Decentralization Conference in Japan, the 2008 spring meeting of Japanese Economic Association, and the 2008 European Meeting of the Econometric Society for helpful comments. We also thank financial support from the Grantsin-Aid for Scientific Research (17730129, 19730145, 19730174, 20530153) and the Inamori Foundation. †College of Economics, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan; khajime@eco.osakafu-u.ac.jp. ‡Faculty of Economics, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan; ohta@eco.wakayama-u.ac.jp. §Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan; sekiguchi@kier.kyoto-u.ac.jp.