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, product adoption and social contagion.

While traditional tools for the analysis of these systems 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 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 social planner designs interventions based on probabilistic instead of exact information about agent’s interactions. I will introduce the tool of “graphon games” as a way to formally describe strategic interactions in this setting and I will illustrate how this tool can be exploited to design interventions. I will cover two main applications: targeted budget allocation and optimal seeding in contagion processes. I will illustrate how the graphon approach leads to interventions that are asymptotically optimal in terms of the population size and can be computed without requiring exact network data.