Cheap talk in a timing game, double layered talk and multilayered talk

My dissertation studies strategic information transmission through costless messages, which is often referred to as "cheap talk". The first chapter studies cheap talk in a setting where time plays an important role. The second chapter studies a situation when a decision maker and an expert communicate through a medium. The third chapter extends the second chapter to multiple mediums.;In the first chapter, when time is incorporated into cheap talk, this kind of game has a special feature. Over the course of the game, the decision maker's action set shrinks as time passes. The expert, who has the information for decision making, chooses a time to send a signal to the decision maker, who does not have any information and seeks advice from the expert to make a timely decision. Then the decision maker chooses a time to take an action, which determines the welfare of both players. I characterize the set of Bayesian equilibria for the case of quadratic utility and a uniform prior. The main findings of this paper are as follows. First, there is a large set of equilibria, which includes all CS equilibria and delegation equilibria. Second, the decision maker must set a T such that she will take action immediately if she does not receive any message before or at T, and the value of T depends on the size of the interest conflict between the two players. Third, the characteristics of the equilibrium highly depend on this stop time. Fourth, the set of action times later than T, but induced by a message sent at time earlier than T, is finite.;The second chapter studies a situation when a decision maker and an expert communicate through a medium, who strategically translates the expert's message to the decision maker. The expert sends a message to the medium, then the medium sends a message to the decision maker based on the message he has received, and finally the decision maker takes action based on the medium's message. By adding a medium in communication, both the expert and the decision maker have to take the medium's personal interests into account. The main findings are as follows. First, in an equilibrium where the expert can control the medium's behavior, with quadratic utility, information loss need not occur and the expert and the decision maker communicate as if they did so directly. Second, the decision maker can improve his welfare by choosing a medium with opposite interests to the expert.;In the third chapter, I study cheap talk with multiple mediums. I show that if all senders have positive bias, then at most one medium will affect the equilibrium. If some have negative bias and some have positive, then at most two mediums are relevant.