2019/12/18 by Damonte, Luca, Como, Giacomo, Fagnani, Fabio
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1912.08631
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.