Correlation Neglect in Games

Abstract: This paper proposes a simple framework to study the effect of correlation neglect on social learning and welfare in games with social incentives. It examines statistical learners (frequentists, Bayesians, etc.) who make decisions based on their peers' actions but overlook the correlation between the actions they observe. A novel solution concept called correlated sampling equilibrium with statistical inference (CoSESI) reveals that correlation neglect affects strategic behavior through persistent overprecision, which leads to polarization and information cascades. CoSESI always exists and differs from existing concepts. It captures the fact that naive beliefs are overly sensitive to correlations, which causes failures of social learning. Applications of CoSESI in matching markets, monopoly pricing, and financial markets demonstrate that correlation neglect bears significant economic consequences.