Equilibrium Pricing in Oligopolistic Data Markets

We study equilibrium pricing in oligopolistic data markets with budget-constrained buyers (e.g., ML 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 need not exist, and in fact no 1.364-approximate equilibrium exists 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 Nash equilibrium). Finally, our simulations demonstrate fast convergence and empirical approximation guarantees that outperform the worst-case bound of 2.

Modern AI companies increasingly buy training data from specialized providers. But data has an unusual property: unlike physical goods, a single dataset can be sold to multiple buyers — economists call this "non-rivalry". This raises a basic question for any data marketplace: when a handful of competing providers each set their own prices, do stable prices ever emerge — where no provider can increase their revenue by changing their dataset's price? We studied markets where sellers price their datasets and budget-limited buyers pick the datasets that best sharpen their predictions. We proved that under the usual "uniform" pricing (same price per data record), stability is not guaranteed — there are markets where for any candidate prices, some seller can always increase their revenue by at least 36%. However, when sellers use slightly richer pricing rules (charging different rates as buyers buy more), an approximate stable outcome always exists: no seller can double their revenue by switching to uniform pricing. Our simulations on a news marketplace for stock prediction show that the gap is typically much smaller, and prices converge quickly. Our findings help understand when data marketplaces can settle into stable prices and how richer pricing schemes aid stability.