Damned If You Do and Damned If You Don\u2019t: Two Masters

We study common agency problems in which principals (groups) make costly commit- ments to incentives that are conditioned on imperfect signals of the agent\u2019s action. Our framework allows for incentives to be either rewards or punishments and an equilibrium al- ways exists. For our canonical example with two principals we obtain a unique equilibrium, which typically involves randomization by both principals. Greater similarity between prin- cipals leads to more aggressive competition. The principals weakly prefer punishment to rewards, sometimes strictly. With rewards an agent voluntarily joins both groups; with pun- ishment it depends on whether severe punishments are feasible and cheap for the principals. We study whether introducing an attractive compromise reduces competition between prin- cipals. Our framework of imperfect monitoring offers a natural perturbation of the standard common agency model, which results in sharper equilibrium predictions. The limit equilib- rium prediction provides support to both truthful equilibria and the competing notion of natural equilibria, which unlike the former may be inefficient