Only Time Will Tell: Credible Dynamic Signaling

Abstract: This paper characterizes informational outcomes in a model of dynamic signaling with vanishing commitment power. It shows that contrary to popular belief, informative equilibria with payoff-relevant signaling can exist without requiring unreasonable off-path beliefs. The paper provides a sharp characterization of possible separating equilibria: all signaling must take place through attrition, when the weakest type mixes between revealing own type and pooling with the stronger types. The framework explored in the paper is general, imposing only minimal assumptions on payoff monotonicity and single-crossing. Applications to bargaining, monopoly price signaling, and labor market signaling are developed to demonstrate the results in specific contexts.