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α: calibrated so average coauthorship-adjusted count equals average raw count
This paper derives the set of equilibria for common agency games in which the principals compete in piece rates and lump sum payments and one principal has incomplete information about the agent's preferences. We show that the uninformed principal's expected payoff function is discontinuous with respect to the identity of the marginal agent type. This discontinuity is shown to support an open set of equilibria. For games in which the first-best equilibrium strategies are measurable with respect to the uninformed principal's information partition, this result implies the existence of an open set of Pareto inefficient equilibria.