This dissertation consists of three chapters, studying questions in dynamic games and information economics. These chapters represent a selection of my research conducted during the period of my PhD studies.
Chapter 1 is motivated by the "starting small" phenomena which are prevalent in long-term relationships. For example, in credit relationships, it is often observed that the credit limit granted to a borrower by a lender tends to increase over time conditional on satisfactory repayment histories. Why does this happen? To provide a novel explanation, we study a repeated lender-borrower game with anonymous re-matching; that is, once an ongoing relationship is terminated, players are rematched with new partners and prior histories are unobservable. We propose an equilibrium refinement based on two assumptions: (a) default implies termination of the current relationship; (b) in a given relationship, a better loan-repayment history implies weakly higher continuation values for both parties. This refinement captures the idea of "justifiable punishments" in repeated games. We show that if players are patient enough and re-matching is sufficiently likely, then the loan size is strictly increasing over time along the equilibrium path of all non-trivial equilibria. As such, this chapter helps explain gradualism in long-term relationships, especially credit relationships.
Chapter 2, based on the joint work with Elliot Lipnowski and Laurent Mathevet, concerns the optimal design of information transmission protocols when the information recipient is rationally inattentive. We develop a model of a well-intentioned principal who provides information to a rationally inattentive agent. Processing information is costly to the agent, but the principal does not internalize this cost. In a world with two states, it is shown that providing full information is universally optimal for the principal, even though the agent will typically not pay full attention. We then introduce a tractable specification with quadratic payoffs and study optimal information provision when full disclosure is not optimal. We characterize incentive compatible information policies, that is, those to which the agent willingly pays full attention. In a leading example with three states, optimal disclosure involves information distortion at intermediate costs of attention. As the cost increases, optimal information abruptly changes from downplaying the state to exaggerating the state.
Chapter 3 naturally extends the theoretical framework introduced in Chapter 2 to a different but relevant setting where the decision interests between the sender and the receiver of information are misaligned. In our model, a Sender (seller) tries to persuade a rationally inattentive Receiver (buyer) to take a particular action (e.g., buying). Learning is costly for the Receiver who can choose to process strictly less information than what the sender provides. In a binary-action binary-state model, we show that optimal disclosure involves information distortion, but to a lesser extent than the case without learning costs; meanwhile, the Receiver processes less information than what he would under full disclosure. While the Sender is always worse off when facing a less attentive Receiver, the amount of information processed in equilibrium varies with learning costs in a non-monotone fashion. As such, this chapter sheds light on how to persuade a rationally inattentive decision maker.
