Efficiency and complexity of price competition among single-product vendors

TL;DR

This paper analyzes the strategic pricing behavior of vendors in competitive marketplaces with identical products, examining equilibrium existence, efficiency, and computational complexity, and explores subsidies to improve outcomes.

Contribution

It introduces a game-theoretic model for vendor pricing, studying equilibrium properties and proposing subsidy mechanisms to enhance market efficiency.

Findings

Equilibria may not always exist or be efficient.

Computational complexity of finding equilibria varies.

Subsidies can improve market outcomes.

Abstract

Motivated by recent progress on pricing in the AI literature, we study marketplaces that contain multiple vendors offering identical or similar products and unit-demand buyers with different valuations on these vendors. The objective of each vendor is to set the price of its product to a fixed value so that its profit is maximized. The profit depends on the vendor's price itself and the total volume of buyers that find the particular price more attractive than the price of the vendor's competitors. We model the behaviour of buyers and vendors as a two-stage full-information game and study a series of questions related to the existence, efficiency (price of anarchy) and computational complexity of equilibria in this game. To overcome situations where equilibria do not exist or exist but are highly inefficient, we consider the scenario where some of the vendors are subsidized in order to keep prices low and buyers highly satisfied.