Dynamic Learning and Pricing with Model Misspecification and Endogeneity Effect

Abstract

In the demand estimation process, it is widely known that price endogeneity, or the correlation between price and demand noise, can cause biased estimation of price elasticity. We study a dynamic pricing model with contextual information and show that price endogeneity can arise in this setting, leading to incorrect estimation of model parameters and potentially suboptimal pricing decisions. To address the endogeneity effect we propose a “Random Price Shock” (RPS) algorithm, which dynamically generates independent price shocks to estimate price elasticity and maximizes revenue while controlling for the endogeneity effect. We show that the RPS algorithm has strong theoretical and numerical performance, and is robust to model misspecification.