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

2025-11-05

AI Summary

This paper addresses the fragmented and unidirectional pricing in machine learning economies, where dataset markets and pre-trained model markets operate independently. We propose the first unified, coupled market mechanism enabling symmetric equilibrium among data sellers, model producers, and model buyers. Methodologically, we establish a closed-loop bidirectional supply–demand mapping: on the supply side, generative models determine model prices; on the demand side, Shapley value theory is employed to retroactively allocate prices to constituent datasets, and we rigorously prove existence, uniqueness, and global convergence of equilibrium using the standard interference function (SIF) framework. Experiments demonstrate that our mechanism significantly improves market fairness and resource allocation efficiency over centralized brokerage and unidirectional pricing baselines. It provides a provably sound, computationally tractable, and scalable theoretical framework and practical paradigm for co-evaluating data and model value.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Privacy

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Pricing data and models separately in ML markets
• Lack of symmetric mechanisms for all market participants
• Need unified equilibrium pricing across coupled transactions

Innovation

• Unified data-model coupled market system
• Supply-demand closed loop with Shapley allocation
• Standard interference function guarantees equilibrium convergence