Signaling private choices

Abstract

For a number of important applications of signaling, it is sometimes more reasonable to assume that the sender rather than nature chooses its unobservable features (e.g. its private choice of quality). In other situations, it makes no sense at all for nature to determine the sender's unobservable features (e.g. its private choice of capacity, investment, contract or price). This paper provides a framework to analyze a wide range of such endogenous signaling problems. An equilibrium concept (Reordering Invariance) is proposed, which is powerful in eliminating unreasonable equilibria and relatively easy to apply. A class of monotone endogenous signaling games is characterized, in which the sender can influence the receivers' actions to its benefit through signaling. For such games, we show that a sender's private choice can still have some commitment value even though it is not observed, and that in equilibrium, the sender's signals must be exaggerated. These points are illustrated with a simple model of costly announcements that applies to the classic time inconsistency problem of monetary policy. The paper also explains how to apply our framework to more complicated settings, including to situations which have not previously been considered as signaling problems (e.g. to loss leader pricing and to the opportunism problem that arises when a manufacturer sells to competing retailers through private contracts).