Chapter 1 studies the credence goods market in a dynamic setting. Complementary to the existing literature that extensively studied credence goods markets in static settings, we develop a dynamic model in which a durable good breaks down stochastically after treatments, and the customer meets the expert recurrently. We assume that the minor treatment alleviates the symptom of the major problem but fails to cure it, increasing the future failure rate. In contrast to the literature, we show that the truth-telling equilibrium never exists under the verifiability assumption, because the standard equal-margin condition fails.

In our dynamic setting, the expert has a stronger incentive to undertreat since undertreatment induces more future business. But on the other hand, the customer becomes less willing to pay for the minor treatment for fear of increased future payments. Therefore, depending on the relative magnitude of these two opposing forces, either Undertreatment or Overtreatment can emerge in equilibrium. Surprisingly, the expert’s incentive to undertreat weakens as the increment of failure rates rises.

Chapter 2 studies a repeated principal-agent relationship in which the agent first collects information and then makes an investment decision n behalf of the principal, utilizing both his private information and informative public opinion. The optimal relational contract may induce the agent to be resistant to public opinion, which we interpret as a form of principal-induced stubbornness. Specially, for intermediate discount factors, it is optimal for the principal to induce stubbornness in the agent when public opinion is neither too precise nor too imprecise. On the other hand, in contrast to findings in the related literature, it is never optimal to induce conservative utilization of the agent’s private signal
due to our introduction of informative public opinion and the stochastic nature of the private signal.

Chapter 3 considers a large society where players search and match to play the voluntarily separable infinitely repeated prisoner’s dilemma game. In-relationship searches are allowed. In contrast to the conventional wisdom that allowing outside options to improve through search could destabilize the extant relationship, we show that such searching opportunities, not to be exercised on the equilibrium path, can promote cooperation and keep the relationship long-lasting.