To investigate the role of trading commissions in broker-investor relationships, I study a dynamic cheap-talk communication game in which a receiver's payoff depends on a stochastic observable state (portfolio position) and a fixed state, which is privately known to the Sender. The position evolves as a Brownian motion, whose evolution can be controlled by the Receiver at a fixed cost paid to the sender. If fully informed, the receiver controls the position in an (s,S) policy. When uninformed, I show that the position has an `informational' value to the Receiver in addition to its inherent value, because it determines the sender's incentives to truthfully report the state. I study Markov Perfect Equilibria where the sender has an option to send uninformative messages, and show that this restricts the set of equilibrium `truth-telling' positions, even though the sender is not able to commit to delaying communication. I extend the model to show analogous results for proportional commissions and stochastic states.
Research In Progress
Dynamic Information Acquisition with Trading Commissions - Slides
I study a dynamic game between an investor and a broker with delegated information acquisition. The investor wants to maintain her portfolio of risky assets at an optimal benchmark level, which is stochastic and unobservable. The broker has the ability to generate public information about the benchmark at a cost, and earns a fixed commission whenever the investor changes her portfolio. I compare this to the case where the investor is able to acquire information herself, and show that with information power, the broker delays information acquisition and the investor increases her trade likelihood. This characterizes the inefficiency in the broker’s actions as compared to the case with the optimal contract, which is a direct payment for research.
Reputational Cheap Talk
I study a dynamic model of reputational cheap talk in which a constant state determines whether a crisis will or will not occur at some random time in the future. Conditional on his ability, a sender becomes increasingly informed about this constant state. A low-ability sender does not receive any information but can send false reports to appear informed. The sender gets a high payoff if the passive receiver's beliefs put more weight on him being of high-ability. I characterize the distribution of the time of false reports by the low-ability sender and show that the distribution of false reports, which the sender makes to pretend that he has become informed, put more weight on earlier times than the true distribution for a high-ability sender. An application on reports by financial experts suggests that they may tend to over-enthusiastically report possible events such as stock booms or crises in order to appear highly skilled.