Risk and security tradeoffs in graphical coordination games

A system whose operation relies on the collective behavior of a population of autonomous decision-makers can be vulnerable to adversarial attacks as well as environmental risks. Such external influences can substantially degrade system efficiency. A system operator may take defensive measures to mitigate the impact of these influences. In this paper we study the effectiveness of such counter-measures, when the underlying system is framed as a graphical coordination game. Here, agents choose among two conventions and derive benefits from coordinating neighbors. System efficiency is measured in terms of the total benefits agents receive in the network relative to the optimal welfare. An adversary can influence the decision-making process of selected agents in the network. The system may alternatively be subject to environmental risks in the form of fixed agents, who do not update their decisions but influence the decisions of others. The system operator aims to protect system efficiency from either adversarial attacks or environmental risks, given uncertainty about the underlying graph topology and severity of influence. Our main contributions characterize the operator's ability to preserve system efficiency, as well as the operator's trade-off between security levels against worst-case adversarial attacks and vulnerability from worst-case environmental risks, and vice versa.