Systemic risk and network intervention
Luca DamonteDepartment of Mathematical Sciences, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, ItalyGiacomo ComoDepartment of Mathematical Sciences, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, ItalyFabio FagnaniDepartment of Mathematical Sciences, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy
ABI
Abstract
We consider a novel adversarial shock/protection problem for a class of network equilibria models emerging from a variety of different fields as continuous network games, production networks, opinion dynamic models. The problem is casted into a min-max problem and analytically solved for two particular cases of aggregate performances: the mean square of the equilibrium or of its arithmetic mean. The main result is on the shape of the solutions, typically exhibiting a waterfilling type structure with the optimal protection concentrated in a proper subset of the nodes, depending significantly on the aggregate performance considered. The relation of the optimal protection with the Bonacich centrality is also considered.
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