Social Influence in Networks

This thesis is composed by three standalone papers. The first chapter is about opinion formation processes. Individuals influence each other according to the network structure. If the network is connected and satisfies other mild assumptions, the society will reach a consensus. Therefore, it is a matter of interest understanding when the network would be connected or not. Here, we develop a model where the network takes place endogenously, and agents update their opinions accordingly. We study general conditions on the initial distribution of opinions such that consensus will be reached. We provide sufficient conditions for connectedness. In the dynamic model we show that polarization both in the transition and the long run. This essay is a joint work with Paolo Pin (Bocconi University). The second chapter is about peer effects. I consider how social pressure affects the strategic network formation process. Agents choose their links subject to mutual consent, and then equilibrium behaviors are determined by an underlying game where agents choose their effort. I provide a characterization result for all pairwise Nash stable network, and use farsightedness to avoid cycles. As an application, I consider peer effects in the classroom. Results suggest that we could set optimal policies to improve outcome of low achievement students through targeted incentives schemes. In the last chapter I focus on the interaction between real and virtual life. To do so I propose a model of search where agents choose in equilibrium how intense is their on-line activity. The outcomes of the game depend on the network, which takes place through a semi-random process. I extend the standard random network formation allowing agents to hold a certain degree of choice. The model allows to track characteristics on the meeting environment and individual preferences that would make virtual and real life substitutes or complements.