Analysis and interventions in large network games: graphon games and graphon contagion

Many of today’s most promising technological systems involve very large numbers of autonomous agents that influence each other and make strategic decisions within a network structure. Examples include opinion dynamics, targeted marketing in social networks, economic exchange and international trade in financial networks, product adoption decisions and social contagion. While traditional tools for network game analysis assumed that a social planner has full knowledge of the network of interactions, when we turn to very large networks two issues emerge. First, collecting data about the exact network of interactions becomes very expensive or not at all possible because of privacy and proprietary concerns. Second, methods for designing optimal interventions that rely on the exact network structure typically do not scale well with the population size. To obviate these issues, in this talk I will present a framework in which the central planner designs interventions based on probabilistic information about agent’s interactions, which can easily be inferred from aggregated data, instead of exact network data. I will introduce the tool of “graphon games” as a way to formally describe strategic interactions in this framework and I will illustrate how this tool can be exploited to design interventions that are robust to stochastic network variations. I will cover two main applications: design of targeted interventions for linear quadratic network games and design of optimal seeding policies for threshold contagion processes. In both cases, I will illustrate how the graphon approach leads to interventions that are asymptotically optimal in terms of the population size and can be easily computed without requiring exact network data.


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