Strategic Equilibrium in Social Networks and Games: Theory and Applications

Abstract

The following is an outline of the four chapters of this dissertation. Chapter 1 shows that subgame perfect equilibrium and weak perfect Bayesian equilibrium require rationality at information sets that are irrelevant for determining whether outcomes are sustained by sequentially rational play. I introduce the concept of a trimmed equilibrium which requires rational play only at relevant information sets. Trimmed equilibrium can show existence of an outcome consistent with sequentially rational play when no equilibrium exists. Chapter 2 provides a noncooperative grounding of weakly pairwise Nash stable networks. I define a modified version of Myerson's linking game and show that the set of its pure strategy Nash equilibrium networks is equivalent to the set of weakly pairwise Nash stable networks. While a weakly pairwise Nash stable network might not exist, a mixed strategy equilibrium of the game I define exists. Chapter 3 shows that in competition between a developed country and a developing country over standards and taxes, the developing country may have a `second mover advantage.' A key feature is that all firms do not unanimously prefer higher standard levels. We introduce this feature to an otherwise familiar model of fiscal competition and obtain three distinct outcomes depending on the level of the cost to firms of `standard mismatch': the outcome may be efficient; the developing country may be a `standard haven'; there may be a `race to the top.' Chapter 4 examines optimal strategies for promoting the diffusion of behavior. I assume that a lobbyist tries to persuade a network of voters to vote for a proposal by targeting influential voters. In networks with a core-periphery structure the lobbyist targets well-connected opponents of the proposal. I also provide bounds on the number of voters that have to be convinced to eventually generate unanimous support and show that more tightly connected groups are harder to convince. Moreover, in any network, after a finite number of periods a voter either continuously supports or opposes the proposal or is a "swing voter" who keeps switching back and forth between two opinions.