Essays on Networks in Economics: Pairwise Influences and Communication Processes

Aquesta tesi estudia dues questions diferents. En primer lloc, les consequencies economiques de les influencies per parelles, enteses com externalitats amb intensitat i signe depenent de la parella dagents considerats. En segon lloc, els efectes de diferents processos de comunicacio en grups petits, i les consequencies per estructures de xarxa optimes en organitzacions informals. En el primer capitol, Pairwise Influences and Bargaining Among the Many, estudio com les influencies per parelles afecten la natura i solucio dels conflictes distributius. El patro dinfluencies per parelles te una estructura de xarxa. Analitzo com la solucio del conflicte distributiu en que els agents han de dividir entre ells un cert nivell de recursos disponibles incorpora el patro heterogeni dinfluencies per parelles en les porcions i utilitats obtingudes. Utilitzo la solucio de Nash com a eina per resoldre el conflicte distributiu. Els resultats es fonamenten en Iindexs de centralitat en xarxes que mesuren la prominencia de cada agent deguda a la seva posicio dins la xarxa que representa lestructura dinfluencies. El capitol On Pairwise Influence Models: Networks and Efficiency proveeix una analisi completa de la relacio entre influencies per parelles i externalitats de xarxa, que tenen en compte tots el nivells defectes indirectes generats pel patro dinfluencies, i una caracteritzacio completa del conjunt dassignacions eficients en el sentit de Pareto per gairebe qualsevol economia amb influencies per parelles en termes de mesures de prestigi, que deriven de la literatura analitica de xarxes socials. El capitol Spatial Spillovers and Local Public Goods analitza questions relacionades amb els efectes dexternalitats espacials en estructures urbanes i la provisio de bens publics locals, sota loptica de models dinfluencies per parelles. Estudio un joc de provisio de bens publics amb externalitats espacials. Els barris escullen quant volen contribuir a la provisio de serveis publics que despres son assignats entre ells amb lus de la solucio de Nash. Analitzo el paper de la distribucio de riquesa i el patro dexternalitats en els nivells de provisio insuficient de be public. En el capitol Communication Processes: Knowledge and Decisions, realitzat amb el professor Antoni Calvo-Armengol, introduim un model de comunicacio en organitzacions informals. Analitzem com diferents processos de comunicacio dinformacio privada impacten en les accions optimes de cada membre. Cada un daquests esquemes dagregacio dinformacio determina la forma en que cada membre construeix le seves creences sobre la tasca a realitzar. Lanalisi introdueix un nou concepte, lindex de coneixement, que agrega en un valor idiosincratic totes les creences de qualsevol ordre per qualsevol proces de comunicacio. En general el joc analitzat te un unic equilibri Bayesia. Laccio dequilibri de cada agent es lineal en el missatge obtingut en el proces de comunicacio, i el pes daquest missatge es precisament lndex de coneixement. Les propietats dunicitat i linealitat de lequilibri Bayesia ens permeten obtenir clares implicacions en termes de benestar, i obtenir diversos resultats destatica comparativa. El darrer capitol, On Optimal Communication Networks, tambe realitzat amb el professor Antoni Calvo-Armengol, es fonamenta en el model i resultats de lanterior capitol per estudiar una familia de processos de comunicacio en xarxa. Obtenim un ordre parcial en el conjunt de xarxes possibles i la nostra analisi mostra que quan hi ha una unica ronda de comunicacio, i un nombre limitat de possibles vincles, lestructura geometrica optima de xarxa que organitza aquests vincles maximitza un index dirregularitat de la xarxa. En canvi, quan el nombre de possibles rondes de comunicacio augmenta, la xarxa optima passa a ser regular. Obtenim aixi, per un conjunt ampli de parametres, un resultat de polaritzacio en termes del nombre de rondes de comunicacio disponibles. 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 agents 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 Calvo-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 Calvo-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.