Signaling Private Choices

For many applications of signalling, senders rather than nature choose unobserved features such as their private choices of quality, capacity, investment, contract, or price, along with other actions that are (partially) observed by receivers. Despite the large number of different applications, these games have not been studied in any systematic way. We identify and study a general class of such games, which we call “endogenous signalling games”. These games normally suffer from a plethora of equilibria. To focus on reasonable equilibria, we propose to solve such games by requiring that the solution be invariant to a particular reordering of the senders’ moves. For a class of single-sender monotone endogenous signalling games, we show that the sender’s private choice can still have some commitment value even though it is not observed and that the sender’s signals must be exaggerated in equilibrium. Applications to loss-leader pricing, costly announcements, limit pricing, advertising, corporate financing, and private contracting are given.