Minimizing network volatility by targeting node-specific interventions
Targeting Interventions for Volatility Reduction in Network Systems - Part I: Idiosyncratic Shocks
Computer Science and Game Theory
Summary
When some parts of a connected system experience sudden changes, these shocks can spread and cause big fluctuations throughout the whole system. The authors study how different points in the network amplify these fluctuations and identify ways to reduce the overall instability by applying limited interventions. They show the best strategies focus first on the most influential nodes, then spread out as more resources are available. They also consider the worst-case scenarios where shocks are chosen to cause maximum disruption, and find similar intervention patterns.
What this means in practice
- •For infrastructure network managers: Identify critical nodes to strengthen for mitigating fluctuations caused by localized disruptions in supply or communication networks.
- •For financial risk teams: Optimize allocation of risk reduction measures across interconnected financial institutions to minimize systemic volatility caused by shocks to individual firms.
Authors
Luca Damonte, Leonardo Cianfanelli, Giacomo Como, Fabio Fagnani
Abstract
We study optimal intervention design problems aimed at minimizing the aggregate volatility in network systems. We consider linear network equilibrium models arising in network games, production networks, and opinion dynamics, where exogenous shocks hitting a few nodes can propagate through the network and cause detrimental systemic effects. Focusing on idiosyncratic shocks, we first identify a general network centrality measure that determines the amplification factor of the variance of each node's shock to the aggregate system volatility, and show that, in relevant special cases, it reduces to Katz-Bonacich, cycle, and concentration centralities. We then consider a system planner who can attenuate the shocks on the nodes, subject to a budget constraint, so as to minimize the aggregate volatility. We solve this problem analytically and show that its solution has a water-filling-type structure: for low budget, the intervention is concentrated on the node(s) maximizing a quantity ω_i that combines the shock's variance, the node's centrality, and the intervention cost; as the budget increases, more and more nodes are targeted, and for sufficiently large budget every node with ω_i > 0 receives an intervention proportional to ω_i. Finally, we study a robust version of the problem, where the planner minimizes the volatility against the worst-case vector of shock variances chosen by an adversary within a given budget. We solve this min-max problem analytically and show that its solution also has a water-filling-type structure, with the ratio between the node's centrality and the square root of the adversarial cost playing the role of ω_i.