Endogenous Diffusion in Social Networks. Two Cases: Infectious Diseases and Sharing of Knowledge

Complex phenomena arising from the interaction of ``elemental'' pieces have been first studied in physics and biology, where such constitutive particles were given deterministic rules for their behavior. In that context it was already clear that even critical outcomes can result on the aggregate level in situations where agents' behaviors are ``mechanic'' and ``simple''. In recent years, inspired by real-world phenomena, economics and other social sciences have also started to play a role in this very wide strand of research. On the one hand, by introducing degrees of rationality in agents' behaviors and, on the other hand, by allowing heterogeneity in their interactions and responses to endogenous and exogenous stimuli. This kind of reasoning has proven itself of particular success when applied in the context of social networks. Research on such intrinsically complex objects blossomed naturally within the realm of sociology, however it was only with the advent of the Internet, with the availability of large databases and the application of mathematical techniques from statistical physics that the field has really started its golden period of prosperity. In this dissertation we contribute to this strand of literature by focusing on diffusive mechanisms that naturally emerge in the context of social networks. The first example is provided by the contagion of diseases channeled through social contacts, with possible straightforward applications to the cases of diffusion of opinions or of bad habits. The second example under study is that of knowledge diffusion (sharing?), which is not only typical of the academic world but also of innovation-seeking environments, such as that of research-and-development firms, where a collaboration network is constituted by the individuals. A common feature of these cases is the fact that economic agents can endogenously and dynamically adapt by changing their (local) network of contacts or their response. In both examples, though, the impact of a single agent's action can reverberate through the whole system via its contacts (and its contacts' contacts, and so on). In the context of social networks, then, it becomes particularly challenging to understand how local features (behaviors or inclinations) may propagate, amplify or dissolute when embedded in the whole environment. One crucial difference with other approaches lies exactly in the fact that ``local'' neighborhoods can indeed be very different from one another and, moreover, very different from the global situation, which is the outcome at an aggregate level. This dissertation is structured as follows. The first chapter describes a model of diffusion of a disease between two different locations, where the agents are able to respond and adapt to this menace. A peculiarity of our model is the possibility of agents of deciding where (i.e. with whom) to interact, in the attempt of avoiding contagion while still obtaining the benefits coming from the interactions with other healthy agents. The analytical results show that such individual-level behaviors have crucially different outcomes depending on the ``world'' these agents are living in: in particular, the two globally different systems considered (one, ``globalized'', where connections between the locations are allowed and the other, ``autarkic'', where they are forbidden) exhibit crucially different resistance to exogenous shocks in the infection rate. Further research in this field is still needed, as this model is one of the few attempts in the economics literature at trying to embed rational and responsive agents in a dynamical model of diffusion on networks. Applications to systemic risk and systemic resistance can benefit from this kind of research as well as analyses of mechanisms where is prevalent the interplay between local versus global forces. The second chapter deals with a classic dilemma in the economics and business literature, that of exploration versus exploitation, and links it to the achievement of results, i.e. to the notion of performance. Specifically, we follow individual scientists throughout their careers and use their co-authorship and citation networks to map their ``knowledge space'', in order to measure their propensity to explore, both in terms of new topics and of new collaborations. Econometric results shows that the relationship between exploration and performance tends to exhibit an inverted-U shape, hence supporting the theory that a ``sweet'' spot where performance is maximized might exist, at least at an individual level. Further research on this topic is still necessary, for example to understand in depth the relationship existing (if any) between forms of ``social exploration'' (i.e. exploration in terms of collaborations and social contacts) and ``scientific exploration'' (i.e. in terms of changes of the subjects studied or fields of expertise). Moreover, the results and techniques developed here can not only be directly applied to bibliometrics studies, but can also be fundamental to give the right incentives (and, possibly, funding) to encourage long-term innovation-seeking behaviors. The third chapter tackles the same research question, but from a different viewpoint: what is the outcome of that analysis when the production units are ``aggregated'' at the level of (departments of) universities? At this aggregate level, it turns out that, in contrast to what seen in the previous chapter, a U-shaped curve characterizes the relationship between performance and exploration. Moreover, this relationship is also complicated by the effects of resources and size of each university. This complication can be seen as evidence of how, at this level, the interplay between economies of scale and economies of scope can generate an overall complex behavior. In this case too, then, the individual-level and the aggregate-level analysis exhibit once again very different outcomes: this underlines even more the complexity that comes out from the interactions in systems composed by different layers and levels