Price of Uncertainty for Consensus Games

Abstract: Many game-theoretic models assume that players have access to accurate information, but uncertainty in observed data is frequently present in real-world settings. In this paper, we consider a model of uncertainty where adversarial perturbations of relative magnitude $1+\varepsilon$ are introduced to players' observed costs. The effect of uncertainty on social cost is denoted as the price of uncertainty. We prove a tight bound on the price of uncertainty for consensus games of $\Theta(\varepsilon^2 n^2)$ for all $\varepsilon = \Omega\mathopen{}\left(n^{-1/4}\right)$. This improves a previous lower bound of $\Omega(\varepsilon^3 n^2)$ as well as a previous upper bound of $O(\varepsilon n^2)$.