Efficiency and complexity of price competition among single-product vendors
This work addresses market inefficiencies for vendors and buyers in AI-driven pricing contexts, but it appears incremental as it builds on existing game-theoretic models without introducing a fundamentally new approach.
The paper tackles the problem of price competition among single-product vendors in a marketplace with unit-demand buyers, modeling it as a two-stage full-information game to analyze equilibrium existence, efficiency (price of anarchy), and computational complexity. It proposes subsidies for some vendors to address situations where equilibria are nonexistent or inefficient, aiming to keep prices low and buyer satisfaction high.
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.