Equilibrium Pricing in Oligopolistic Data Markets

2026-08-14

AI Summary

This study addresses the absence of exact Nash equilibria in oligopolistic data markets caused by the non-rivalrous nature of data by investigating pricing mechanisms under budget constraints. We propose a piecewise linear convex pricing strategy and theoretically prove that this mechanism guarantees the existence of a 2-approximate Nash equilibrium against uniform deviations, thereby resolving equilibrium challenges inherent in uniform pricing. Numerical simulations further demonstrate rapid algorithmic convergence, with empirical approximation ratios significantly outperforming theoretical worst-case bounds. By establishing constant-factor approximate stability, this work introduces a novel paradigm for data market pricing that effectively integrates rigorous theoretical guarantees with computational efficiency.

Abstract

We study equilibrium pricing in oligopolistic data markets with budget-constrained buyers (e.g., machine learning companies purchasing data to improve model accuracy) and strategic data sellers. Sellers compete by setting prices for their datasets, giving rise to a pricing game whose pure Nash equilibria correspond to equilibrium prices. While equilibrium prices are guaranteed for rivalrous goods via competitive equilibrium, we show that the non-rivalry of data fundamentally alters this picture: an exact Nash equilibrium (NE) need not exist, and in fact, 1.363-approximate NE may also not exist under uniform pricing. We therefore investigate relaxed equilibrium notions. Allowing sellers to use beyond-uniform pricing---specifically, piecewise-linear convex pricing functions---guarantees approximate stability within a constant factor: there exists a pricing profile in which no seller can improve revenue by a factor of two by deviating to any uniform price (a 2-approximate NE against uniform deviations). Finally, our simulations demonstrate fast convergence and empirical approximation guarantees that outperform the worst-case bound of 2.

Problem

• Oligopolistic Data Markets
• Equilibrium Pricing
• Non-rivalry of Data
• Nash Equilibrium Existence

Innovation

• Oligopolistic Data Markets
• Non-rivalry of Data
• Piecewise-linear Convex Pricing
• Approximate Nash Equilibrium
• Equilibrium Pricing