Only Time Will Tell: Credible Dynamic Signaling

This paper explores a model of dynamic signaling without commitment. It is known that separating equilibria do not exist if the sender cannot commit to future costly actions, since no single action can have enough weight to be an effective signal. This paper, however, shows that informative and payoff-relevant signaling can occur even without commitment and without resorting to unreasonable off-path beliefs. Such signaling can only happen through attrition, when the weakest type mixes between revealing own type and pooling with the stronger types. The possibility of full information revelation in the limit hence depends crucially on the assumptions about the state space. We illustrate the results by exploring a model of dynamic price signaling and show that prices may be informative of product quality even if the seller cannot commit to future prices, with both high and low prices being able to signal high quality.