Pricing Strategy versus Heterogeneous Shopping Behavior under Market Price Dispersion

Abstract

We consider the ubiquitous problem of a seller competing in a market of a product with dispersed prices and having limited information about both his competitors’ prices and the shopping behavior of his potential customers. Given the distribution of market prices, the distribution of consumers’ shopping behavior, and the seller’s cost as inputs, we find the computational solution for the pricing strategy that maximizes his expected profits. We analyze the seller’s solution with respect to different exogenous perturbations of parametric and functional inputs. For that purpose, we produce synthetic price data using the family of Generalized Error Distributions that includes normal and quasiuniform distributions as particular cases, and we also generate consumers’ shopping data from different behavioral assumptions. Our analysis shows that, beyond price mean and dispersion, the shape of the price distribution plays a significant role in the seller’s pricing solution. We focus on the seller’s response to an increasing diversity in consumers’ shopping behavior. We show that increasing heterogeneity in the shopping distribution typically lowers seller’s prices and expected profits.