Resource Allocation in Contagious Networks

Abstract

We study the problem of allocating limited preventive resources for a planner to mitigate the impact of a disruptive shock. The shock is propagated through an interaction network that connects entities, which are grouped into different sectors. Each of the entities may be hit by the shock with a certain probability, which is determined by the probability that it is infected by other entities or from outside this system. Upgrading the prevention can reduce the loss from being infected but incurs a sector-dependent cost. Due to the limited availability of preventive resources, the planner has to prioritize different sectors in resource allocation to pursue a utilitarian or egalitarian objective while the entities make independent decisions on prevention upgrading. We obtain the optimal allocation policy under utilitarianism, which prioritizes sectors with a high-cost reduction from prevention upgrading while jointly considering vulnerability and transmissivity. We also find that the impact probability of entities can be approximated by their weighted Bonacich centrality in the weighted interaction network. Moreover, in a similar vein, we obtain the optimal policy in an explicit form when the planner pursues egalitarianism, which aims to equalize the eventual costs of different sectors after resource allocation. We calibrate our model using the data of New York City collected during the COVID-19 pandemic and identify the performance improvement of our proposed policies relative to the current vaccination practice, which is primarily based on the vulnerability. We find that the performance improvement of the optimal policy over the current practice under the utilitarian (resp., egalitarian) objective increases (resp., decreases) in the lock-down level of society. That implies under the utilitarian (resp., egalitarian) goal, the current vaccination practice performs reasonably well when little (resp., significant) travel restriction is imposed.

Note:
Funding Information: None, for myself and all my co-authors (cc-ed).

Declaration of Interests: No other conflicts declared.

Keywords: network, resource allocation, disruption, security, vaccination, priority

JEL Classification: D71, D85, I18, L88