ICML 2026 paper: Data market pricing has no exact Nash equilibrium

In a new paper presented at ICML 2026, Bhaskar Ray Chaudhury, Jugal Garg, Eklavya Sharma, and Jiaxin Song tackle a fundamental question: how do sellers price data when buyers are machine learning companies with fixed budgets? Unlike traditional goods, data is non-rival—it can be sold to multiple buyers without depletion. The authors formally model this as a pricing game and prove a stark negative result: pure Nash equilibria are not guaranteed, and under uniform pricing (a single price per dataset), no 1.363-approximate equilibrium may exist either. This means that simple pricing strategies can lead to unstable markets where sellers keep undercutting each other or where no price profile is rational for everyone.

To escape this impossibility, the team allows sellers to use piecewise-linear convex pricing functions—a more flexible scheme where the total cost buyers pay grows progressively with the amount of data purchased. They prove this guarantees a 2-approximate Nash equilibrium against uniform deviations: no seller can more than double their revenue by switching to any uniform price. Crucially, their simulations on synthetic markets show convergence is fast and the empirical approximation factor is often much better than the worst-case 2. The work gives data marketplaces a concrete pricing design rule and opens the door for future research on relaxed equilibrium notions tailored to non-rival information goods.