Communication, elicitation, and the value of information

The three chapters of this dissertation explore the value of information in a variety of settings. In each chapter there is a sender (or many senders who has (have access to information and a single receiver who depends on the sender for information. In the first chapter I modify an old question of Frank P. Ramsey, originally asked in the decision problem environment, to the communication game setting, in which an informed sender communicates to a decision maker (receiver, who takes an action that affects both players' welfare. Namely, I ask, ``if information is free prior to a communication game, then does it benefit the receiver in expectation to acquire it?" I show that the answer to this question is not generally yes. I provide tight sufficient conditions that guarantee that the value of information is positive. In the second chapter, I continue to explore communication games. I study how the receiver can acquire more information from the sender by reducing her own ability to observe what the agent transmits. I find that that under broad conditions, the receiver can do just as well as if she could commit to a rule mapping the sender's message to actions: information design is just as good as full commitment. I also investigate how the ability of the receiver to choose what she can see of the sender's message affects the answer to the question asked in the first chapter about the value of information. These broad conditions guarantee that the value of information is always positive. The third chapter departs from the setting of the other two. There, I study an oligopolistic setting in which ex-ante symmetric firms compete via information provision to attract a consumer. I explore how search frictions affect the firms' information provision policies, which are chosen in order to entice the consumer to visit. I find that when the expected quality of the product is sufficiently high, there is a unique symmetric equilibrium in which firms are fully informative. There, a small search cost leads to the perfect competition level of information provision--consumers gain when firms are forced to compete on information. Conversely, in the low and medium expected quality cases there are no pure strategy equilibria. Instead, firms mix over a continuum of levels of information: in the low expected quality case they provide full information with probability zero; and in the medium expected quality case they provide full information with positive probability.Economic