Price Competition Under A Consider-Then-Choose Model With Lexicographic Choice

TL;DR

This paper analyzes how sellers set prices in a competitive market where customers consider multiple attributes and choose based on a lexicographic ranking, providing a structural characterization of equilibria and demonstrating convergence of pricing dynamics.

Contribution

It introduces a new consider-then-choose model with lexicographic preferences, characterizes equilibria, and proves convergence of gradient-based pricing dynamics.

Findings

Equilibria can be characterized structurally.

Gradient dominance condition enables efficient equilibrium computation.

Gradient-based dynamics converge to equilibria in the model.

Abstract

The sorting and filtering capabilities offered by modern e-commerce platforms significantly impact customers' purchase decisions, as well as the resulting prices set by competing sellers on these platforms. Motivated by this practical reality, we study price competition under a flexible choice model: Consider-then-Choose with Lexicographic Choice (CLC). In this model, a customer first forms a consideration set of sellers based on (i) her willingness-to-pay and (ii) an arbitrary set of criteria on items' non-price attributes; she then chooses the highest-ranked item according to a lexicographic ranking in which items with better performance on more important attributes are ranked higher. We provide a structural characterization of equilibria in the resulting game of price competition, and derive an economically interpretable condition, which we call gradient dominance, under which equilibria can be computed efficiently. For this subclass of CLC models, we prove that distributed gradient-based pricing dynamics converge to the set of equilibria. Extensive numerical experiments show robustness of our theoretical findings when gradient dominance does not hold.