Equilibrium informativeness in veto games

In a veto game a biased expert recommends an action that an uninformed decision maker can accept or reject for an outside option. The arrangement is ubiquitous in political institutions, corporations, and consumer markets but has seen limited use in applications due to a poor understanding of the equilibrium set and an ensuing debate over selection. We develop a simple method to construct every veto equilibrium and identify the most informative equilibrium in a setting that spans prior work. We show that Krishna and Morgan's (2001) equilibrium is maximally informative and strengthen Dessein's (2002) comparison of full delegation and veto. In an application we study the relationship between a patient and a doctor with a financial incentive to overtreat, and show that the doctor's bias harms the patient both through excessive treatment and information loss, that the latter can be substantial, and that insurance benefits both parties by improving communication.