Market Participation under Delegated and Intrinsic Common Agency

In a stylized model of common agency with two competing principals and a privately informed agent, we study how competition in nonlinear pricing affects the measure of agents who participate. Two forms of competition are examined. When participation is restricted to all-or-nothing (what has been called “intrinsic” agency), the agent must choose between both principal’s contracts or selecting her outside option; when the agent is afforded the additional possibilities of choosing only one principal’s contract (“delegated” agency), competition operates on a more intense level. Unlike previous analyses of common agency that focused on marginal allocation distortions and found that the delegated and intrinsic agency games have identical outcomes, we find that two games have distinct predictions for participation. We derive the following results: When the principals’ contracting variables are substitutes on the intensive margin, we find that equilibrium outcome in the intrinsic agency game always induces more distortion in participation relative to the monopoly outcome, and the monopoly outcome induces still more participation distortion relative to the outcome under delegated agency. In the case where the contracting variables are complements on the intensive margin, the participation outcome is the same in the delegated and the intrinsic games, and this outcome exhibits a greater participation distortion than what a monopolist would choose. The intuition for these results is closely tied with the observation that intrinsic agency is strategically equivalent to delegated agency when the contracting variables are Leontief complements in the agent’s utility function on the extensive margin. Seen in this light, such complementarity on the extensive margin generates distortions in the extensive consumption decision (i.e., participation rate) as expected.