# Essays on Network Formation

## Abstract

This dissertation contains two essays which examine the roles that individual incentives, competition, and information play in network formation. In the first essay, I examine a model in which two competing groups offer different allocation rules that may depend on the network of connections among the individuals that make up each group. I assume the existence of a single divisible good, such as a monetary prize, which will be divided amongst the members of the winning network. The probability of winning the prize will depend on the network sizes. I examine two well-known allocation rules: the Myerson value and the egalitarian rule. I prove existence of equilibria and characterize the properties of the two networks. The implications of the equilibria networks for the outcome of the contest are discussed. I find that the winning probability of the network using the Myerson value has an upper bound very close to one half. There is no such upper bound for the network using the egalitarian rule.

In my second essay, I examine a dynamic model of network formation in which individuals use reinforcement learning to choose their actions. Typically, economic models of network formation assume the entire network structure to be known to all individuals involved. The introduction of reinforcement learning allows us to relax this assumption. Through the use of a state-dependent reinforcement learning rule, one may allow for varying degrees of information available to the agents. Three informational settings are examined and I determine what networks, if any, each model may converge to in the limit. The long-run behavior of each model is examined through the use of simulations and compared to one another. I find that amount and type of information agents have access plays an important role in which networks emerge when there is no dominant strategy for the agents choosing links. If there is a dominant link choosing strategy, the most efficient network structure quickly emerges in each informational setting.

Together, these essays investigate how information, incentives, and competition may affect network formation. Individual incentives in the presence of competition can create tension between an individual's social ties and the overall network size. Information plays a key role in the emergent network topologies when there are no dominate network building strategies.