On the Existence and Complexity of Core-Stable Data Exchanges

2025-09-19

AI Summary

This paper addresses core stability in data exchange—ensuring no coalition of participants can deviate profitably from the global mechanism. It introduces cooperative game-theoretic core stability to data exchange for the first time, formulating a multi-agent utility model that jointly captures concave benefits and convex costs. Leveraging Scarf’s theorem and the pivoting algorithm, the authors prove existence of stable exchange allocations and design a computationally implementable solution algorithm. Further, integrating PAC learning with stochastic discovery models, they rigorously establish PPAD-hardness of the problem, thereby characterizing its computational complexity lower bound. The work delivers the first theoretical framework for market-oriented data allocation that simultaneously guarantees existence, provides constructive computability analysis, and precisely delineates computational hardness.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The rapid growth of data-driven technologies and the emergence of various data-sharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents -- or groups of agents -- from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data. The net utility of an agent is payoff minus the cost. We adapt the classical notion of core-stability from cooperative game theory to data exchange. A data exchange is core-stable if no subset of agents has any incentive to deviate to a different exchange. We show that a core-stable data exchange is guaranteed to exist when agents have concave payoff functions and convex cost functions -- a setting typical in domains like PAC learning and random discovery models. We show that relaxing either of the foregoing conditions may result in the nonexistence of core-stable data exchanges. Then, we prove that finding a core-stable exchange is PPAD-hard, even when the potential blocking coalitions are restricted to constant size. To the best of our knowledge, this provides the first known PPAD-hardness result for core-like guarantees in data economics. Finally, we show that data exchange can be modelled as a balanced $n$-person game. This immediately gives a pivoting algorithm via Scarf's theorem cite{Scarf1967core}. We show that the pivoting algorithm works well in practice through our empirical results.

Problem

• Ensuring stable data exchanges where agents balance data acquisition benefits against sharing costs
• Studying existence of core-stable exchanges when no agent subset has incentive to deviate
• Analyzing computational complexity of finding core-stable exchanges under various function conditions

Innovation

• Core-stable data exchange model from cooperative game theory
• Existence guarantees with concave payoff and convex cost functions
• PPAD-hardness proof and practical pivoting algorithm via Scarf