Essays on Networks in Economics: Pairwise Influences and Communication Processes

Abstract

This thesis addresses two different questions. First, the economic consequences of pairwise influences, understood as externalities which intensity and sign depend on the pair of agents considered. Second, the effects of different communication processes in small groups, and its consequences for the optimal inner network structure of informal organizations. In the first chapter "Pairwise Influences and Bargaining Among the Many" we analyze how pairwise influences affect the nature and solution of distributional conflict. The pattern of pairwise influences takes the form of a weighted and directed network. When agents have to divide some available resource among them, pairwise influences affect the nature of this distributional conflict. We analyze how the solution to this conflict maps the heterogeneous pattern of pairwise influences to shares and utilities obtained. We use the Nash bargaining solution as the solution to distributional conflict. Our results rely on network centrality indexes that measure each agent's prominence due to his position in the networked influence structure. The chapter "On Pairwise Influence Models: Networks and Efficiency" provides a complete analysis of the mapping from pairwise influences to network externalities, that account for all levels of indirect effects generated by the pat-tern of influences, and a complete characterization of the set of Pareto efficient allocations for almost every economy with pairwise influences in terms of prestige measures, derived from the literature on social network analysis. The chapter "Spatial Spillovers and Local Public Goods" analyzes issues related to the effects of spatial spillovers in urban structure and the provision of local public goods under the light of pairwise influence models. We analyze a local public good provision game with spatial spillovers. Neighbourhoods choose how much they want to contribute to the provision of public services that later on are assigned to them with the use of the Nash bargaining solution. We analyze the role of the wealth distribution and the pattern of spatial spillovers in the levels of underprovision. In the chapter "Communication Processes: Knowledge and Decisions", in joint work with my advisor Antoni Calvó-Armengol, we introduce a model of communication in informal organizations. We analyze how different communication processes of private information impact the optimal actions of each member. Each decentralized information-sharing scheme determines the way in which each member constructs his beliefs on the task to be performed. The analysis introduces a new concept, the knowledge index, that sums up in an idiosyncratic value these higher order beliefs for each possible communication process. In most cases the game has a unique Bayesian equilibrium. The equilibrium action of each agent is linear in the communication report each agent obtains, and this report is, precisely, weighted by the knowledge index. The uniqueness and linearity properties of the Bayesian equilibrium allow for clear welfare implications in our analysis, and to obtain different comparative statics results. The last chapter, "On Optimal Communication Networks," also in joint work with professor Antoni Calvó-Armengol, builds on the model and results developed in the previous chapter to study a family of networked communication processes. We obtain a partial order on the set of possible networks and our analysis shows that when there is one unique round of communication, and there is a fixed supply of possible links, the optimal geometric arrangement of these links maximizes a network span index, a measure of network irregularity. Instead, when the number of possible communication rounds increases the optimal network is regular. Hence, we obtain for a wide set of parameters, a polarization result in terms of the number of available rounds to communicate.

Date of Award	28 May 2007
Original language	Undefined/Unknown
Supervisor	Antoni Calvó Armengol (Director)