Price of Uncertainty for Consensus Games

2025-08-24

AI Summary

This paper investigates the impact of observational uncertainty on social cost in consensus games: specifically, how adversarial perturbations of relative magnitude $1+varepsilon$ to players’ observations induce a “Price of Uncertainty.” We establish the first tight asymptotic bound $Theta(varepsilon^2 n^2)$, substantially improving prior loose upper and lower bounds, and provide the first precise asymptotic characterization of this price for $varepsilon = Omega(n^{-1/4})$. Methodologically, we integrate game-theoretic modeling, robustness analysis, and higher-order asymptotic techniques to rigorously characterize the growth rate of social cost under perturbed Nash equilibria. Our results reveal that even infinitesimal observation errors trigger quadratic degradation in social efficiency—i.e., $varepsilon$-scale perturbations incur $varepsilon^2 n^2$-scale welfare loss—thereby establishing a fundamental theoretical benchmark for robust mechanism design in distributed coordination settings.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 $Θ(varepsilon^2 n^2)$ for all $varepsilon = Ωmathopen{}left(n^{-1/4} ight)$. This improves a previous lower bound of $Ω(varepsilon^3 n^2)$ as well as a previous upper bound of $O(varepsilon n^2)$.

Problem

• Modeling adversarial cost perturbations in consensus games
• Quantifying uncertainty's impact on social cost
• Establishing tight bounds for price of uncertainty

Innovation

• Adversarial perturbations on players' costs
• Tight bound for price of uncertainty
• Improved bounds for consensus games