Market participation in delegated and intrinsic common‐agency games

We study how competition in nonlinear pricing between two principals (sellers) affects market participation by a privately informed agent (consumer). When participation is restricted to all or nothing (“intrinsic” agency), the agent must choose between both principals' contracts and selecting her outside option. When the agent is afforded the additional possibilities of choosing only one contract (“delegated” agency), competition is more intense. The two games have distinct predictions for participation. Intrinsic agency always induces more distortion in participation relative to the monopoly outcome, and equilibrium allocations are discontinuous for the marginal consumer. Under delegated agency, relative to monopoly, market participation increases (respectively, decreases) when contracting variables are substitutes (respectively, complements) on the intensive margin. Equilibrium allocations are continuous for the marginal consumer and the range of product offerings is identical to both the first‐best and the monopoly outcome.