First, motivated by applications in high voltage electric grids, I will discuss interventions aimed at ensuring robust synchronicity in networks of coupled phase-oscillators. Specifically, I will discuss how to optimal allocate network edge weights to minimize a measure of network vulnerability proposed by Tyloo et. al, quantifying how much a small perturbation to a phase-oscillator's natural frequency impacts the system's global synchronized frequencies. I will show that this problem can be reformulated as a tractable semidefinite programming problem and I will illustrate how the obtained result can support optimal placement of renewable generation.

Second, I will consider strategic decision making in social and economic networks. In this case, the underlying network of interactions may be unknown, as collecting exact network data might be either too costly or impossible due to privacy concerns. Moreover, methods for designing optimal interventions that rely on the exact network data typically do not scale well with the population size. To obviate these issues, I will introduce the tool of “graphon games” as a way to formally describe strategic interactions in uncertain network settings and I will illustrate how this tool can be exploited to design interventions that are asymptotically optimal in terms of the population size and can be efficiently computed without requiring exact network data.

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