This thesis considers two applications in dynamics economic models with many agents. The dynamics of the economic systems under consideration are intractable since they depend on the (stochastic) outcomes of the agents' actions. However, as the number of agents grows large, approximations to the aggregate behavior of agents come to light. I use this observation to characterize market dynamics and subsequently to study these applications.
Chapter 2 studies the problem of devising a pricing strategy to maximize the revenues extracted from a stream of consumers with heterogenous preferences. Consumers, however, do not know the quality of the product or service and engage in a social learning process to learn it. Using a mean-field approximation the transient of this social learning process is uncovered and the pricing problem is analyzed.
Chapter 3 adds to the previous chapter in analyzing features of this social learning process with finitely many agents. In addition, the chapter generalizes the information structure to include cases where consumers take into account the order in which reviews were submitted.
Chapter 4 considers a model of dynamic oligopoly competition in the spirit of models that are widespread in industrial organization. The computation of equilibrium strategies of such models suffers from the curse of dimensionality when the number of agents (firms) is large. For a market structure with few dominant firms and many fringe firms, I study an alternative equilibrium concept in which fringe firms are represented succinctly with a low dimensional set of statistics. The chapter explores how this new equilibrium concept expands the class of dynamic oligopoly models that can be studied computationally in empirical work.