Hold-up in vertical hierarchies with adverse selection

•A three-stage sequential game with hold-up and adverse selection is studied.•The principal's capital investment implies a more favorable distribution of types.•The regulator's trade-off concerns distortions, expected rent and investment.•Quantities of first best are not socially desirable.•The allocation of bargaining power is not in favor of one single party.

This paper studies bargaining with hold-up in presence of adverse selection and endogenous type distribution. With limited liability for the agent, quantities of first best are not socially optimal. The allocation of bargaining power is never completely in favor of one party.