This thesis studies optimal stopping problems for strategic agents in the context of two economic applications: experimentation in a competitive market and information exchange in social networks. The economic agents (firms in the first application, individuals in the second) take actions, whose payoffs depend on an unknown underlying state. Our framework is characterized by the following key feature: agents time their actions to take advantage of either the outcome of the actions of others (experimentation model) or information obtained over time by their peers (information exchange model). Equilibria in both environments are typically inefficient, since information is imperfect and, thus, there is a benefit in being a late mover, but delaying is costly. More specifically, in the first part of the thesis, we develop a model of experimentation and innovation in a competitive multi-firm environment. Each firm receives a private signal on the success probability of a research project and decides when and which project to implement. A successful innovation can be copied by other firms. We start the analysis by considering the symmetric environment, where the signal quality is the same for all firms. Symmetric equilibria (where actions do not depend on the identity of the firm) always involve delayed and staggered experimentation, whereas the optimal allocation never involves delays and may involve simultaneous rather than staggered experimentation. The social cost of insufficient experimentation can be arbitrarily large. Then, we study the role of simple instruments in improving over equilibrium outcomes. We show that appropriately-designed patents can implement the socially optimal allocation (in all equilibria) by encouraging rapid experimentation and efficient ex post transfer of knowledge across firms. In contrast to patents, subsidies to experimentation, research, or innovation cannot typically achieve this objective. We also discuss the case when signal quality is private information and differs across firms. We show that in this more general environment patents again encourage experimentation and reduce delays. In the second part, we study a model of information exchange among rational individuals through communication and investigate its implications for information aggregation in large societies. An underlying state (of the world) determines which action has higher payoff. Agents receive a private signal correlated with the underlying state. They then exchange information over their social network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking an action that is close to optimal converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the social network most agents are a short distance away from "information hubs", which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication is not always optimal, when the communication network induces asymptotic learning (in a large society), truthful communication is an equilibrium. Then, we discuss the welfare implications of equilibrium behavior. In particular, we compare the aggregate welfare at equilibrium with that of the optimal allocation, which is defined as the strategy profile a social planner would choose, so as to maximize the expected aggregate welfare. We show that when asymptotic learning occurs all equilibria are efficient. A partial converse is also true: if asymptotic learning does not occur at the optimal allocation and an additional mild condition holds at an equilibrium, then the equilibrium is inefficient. Furthermore, we discuss how our learning results can be applied to several commonly studied random graph models, such as preferential attachment and Erdos-Renyi graphs. In the final part, we study strategic network formation in the context of information exchange. In particular, we relax the assumption that the social network over which agents communicate is fixed, and we let agents decide which agents to form a communication link with incurring an associated cost. We provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results if social cliques are neither too numerous nor too large, in which case communication across cliques is encouraged.
