Price Competition in Linear Fisher Markets: Stability, Equilibrium and Personalization

TL;DR

This paper investigates price competition in linear Fisher markets with strategic sellers, revealing how personalization affects market stability and efficiency through algorithmic and economic analysis.

Contribution

It introduces a new model for strategic seller behavior in Fisher markets, highlighting the impact of personalization on market outcomes and connecting to computational problems.

Findings

Competitive equilibrium remains stable under equal treatment of buyers.

Personalization by sellers increases market unpredictability and reduces efficiency.

The study establishes algorithmic complexity results and links to stable matching and network flow problems.

Abstract

Linear Fisher market is one of the most fundamental economic models. The market is traditionally examined on the basis of individual's price-taking behavior. However, this assumption breaks in markets such as online advertising and e-commerce, where several oligopolists dominate the market and are able to compete with each other via strategic actions. Motivated by this, we study the price competition among sellers in linear Fisher markets. From an algorithmic game-theoretic perspective, we establish a model to analyze behaviors of buyers and sellers that are driven by utility-maximizing purposes and also constrained by computational tractability. The main economic observation is the role played by personalization: the classic benchmark market outcome, namely competitive equilibrium, remains to be a steady-state if every buyer must be treated "equally"; however, sellers have the incentive to personalize, and as a result the market would become more unpredictable and less efficient. In addition, we build a series of algorithmic and complexity results along the road to justify our modeling choices and reveal market structures. We find interesting connections between our model and other computational problems such as stable matching, network flow, etc. We believe these results and techniques are of independent interest.