Production Externalities and Two-way Distortion in Principal-multi-agent Problems

This paper studies an otherwise standard principal-agent problem with hidden information, but whether there are positive production externalities between agents: the output of any agent depends positively on the e¤ort expended by other agents. It is shown that the optimal contract for the principal exhibits two-way distortion: the e¤ort of any agent is oversupplied (relative to the ...rst-best) when his marginal cost of e¤ort is low, and undersupplied his marginal cost of e¤ort is high. This pattern of distortion cannot otherwise arise in optimal singleor multi-agent incentive contracts, unless there are countervailing incentives. However, unlike the countervailing incentives case, the pattern of distortion is robust to the precise form of the externality. ¤I would like to thank an anonymous referee for very valuable comments.