Efficiency in Repeated Partnerships

Two partners contribute to a common project over time. The value of the project is determined by their aggregate effort and a common productivity parameter about which each partner is privately informed. At each instant, the two partners observe a noisy public signal of total effort. An equilibrium of this game is Markov if agents’ effort choices depend only on the beliefs about the value of the project and calendar time. We characterize the linear Markov equilibrium as the solution to a nonlinear boundary value problem. Equilibrium is unique if agents are symmetric. The equilibrium features a mutual encouragement effect, as agents exaggerate their effort to signal their private information, which counteracts free-riding incentives. If the project lasts sufficiently long, the diffused information structure approximates the first-best in terms of welfare. If instead of distributed private information, one agent has all the information about the productivity parameter, the excessive signalling effect is accentuated. As a result, the centralized information structure can yield output levels above the first best.