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

arXiv: https://arxiv.org/abs/2511.03368 · HTML: https://mlsanity.com/paper/2511.03368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [A Survey on Data Pricing: from Economics to Data Science](https://mlsanity.com/paper/2009.04462/) (2020)
- [Model-based Pricing for Machine Learning in a Data Marketplace](https://mlsanity.com/paper/1805.11450/) (2018)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [Golden Grain: Building a Secure and Decentralized Model Marketplace for MLaaS](https://mlsanity.com/paper/2011.06458/) (2020)
- [Semi-Private Computation of Data Similarity with Applications to Data Valuation and Pricing](https://mlsanity.com/paper/2206.06650/) (2022)
- [FLMarket: Enabling Privacy-preserved Pre-training Data Pricing for Federated Learning](https://mlsanity.com/paper/2411.11713/) (2024)
- [Enhancing Trust in AI Marketplaces: Evaluating On-Chain Verification of Personalized AI models using zk-SNARKs](https://mlsanity.com/paper/2504.04794/) (2025)

## Abstract (arXiv)

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.