Essays on network theory and applications

Abstract

This thesis consists of three essays centering on network theory. In the first essay, we use a network model to show how homophily, conjoined with conformity, may shape political divisions along ethnic lines in multi-ethnic societies. We find that the decisive factor is not simply the degree of homophily but the presence of monotone agents, who are only connected with their own types. When there is no monotone agent, even if the level of homophily is unbounded, ethnic divisions can be avoided. The presence of a few monotone agents necessarily divides a sparsely integrated society along ethnic lines. The second essay examines both theoretically and empirically (strong) Nash equilibrium of the free labor mobility network formation game. First, we design a network formation game in which each country's action is a choice of a mobility network between a subset of countries. The utility of each country is determined by a country specific threshold level of absorption ratio and net labor ows. We theoretically characterize all stable and optimal mobility networks under speci fic assumptions. In our empirical analysis, we focus on EU and EFTA member countries. We observe that some specific countries incur the maximum loss in the grand mobility network according to our model. These countries turnout to be the ones in which reintroduction of quotas on migration is approved via referendum. In the third essay, we examine a normal form game of network formation due to Myerson (1991). All players simultaneously announce the links they wish to form. A link is created if and only if there is mutual consent for its formation. The empty network is always a Nash equilibrium of this game. We define a refinement of Nash equilibria that we call trial perfect. We show that the set of networks which can be supported by a pure strategy trial perfect equilibrium coincides with the set of pairwise-Nash equilibrium networks, for games with link-responsive payoff functions.