TripleWin: Fixed-Point Equilibrium Pricing for Data-Model Coupled Markets

TL;DR

This paper introduces a unified market mechanism for data and model trading in machine learning, ensuring fair, convergent pricing through a fixed-point equilibrium approach.

Contribution

It proposes a symmetric, coupled pricing mechanism for data and models that guarantees convergence and fairness, unlike previous broker-centric methods.

Findings

The mechanism guarantees existence and uniqueness of equilibrium prices.

Experiments show efficient convergence of the proposed pricing scheme.

The approach improves fairness over baseline methods.

Abstract

The rise of the machine learning (ML) model economy has intertwined markets for training datasets and pre-trained models. However, most pricing approaches still separate data and model transactions or rely on broker-centric pipelines that favor one side. Recent studies of data markets with externalities capture buyer interactions but do not yield a simultaneous and symmetric mechanism across data sellers, model producers, and model buyers. We propose a unified data-model coupled market that treats dataset and model trading as a single system. A supply-side mapping transforms dataset payments into buyer-visible model quotations, while a demand-side mapping propagates buyer prices back to datasets through Shapley-based allocation. Together, they form a closed loop that links four interactions: supply-demand propagation in both directions and mutual coupling among buyers and among sellers. We prove that the joint operator is a standard interference function (SIF), guaranteeing existence, uniqueness, and global convergence of equilibrium prices. Experiments demonstrate efficient convergence and improved fairness compared with broker-centric and one-sided baselines. The code is available on https://github.com/HongrunRen1109/Triple-Win-Pricing.