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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 in which agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and incurs a cost when sharing its own data. The net utility of an agent is defined as its payoff minus its cost. We adapt the classical notion of core stability from cooperative game theory to the setting of data exchange. A data exchange is said to be core-stable if no subset of agents has an 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 that is typical in domains such as PAC learning and random discovery models. We further show that relaxing either of these conditions can result in the nonexistence of core-stable data exchanges. We then prove that finding a core-stable data exchange is PPAD-hard, even when the set of potential blocking coalitions is restricted to groups of constant size. To the best of our knowledge, this is the first known PPAD-hardness result for core-like stability guarantees in data economics. Finally, we show that data exchange can be modeled as a balanced n-person game. This immediately yields a pivoting algorithm via Scarf’s theorem from 1967 on the core. We demonstrate through empirical results that this pivoting algorithm performs well in practice. 

Federated learning (FL) is a popular collaborative learning paradigm, whereby agents with individual datasets can jointly train an ML model. While higher data sharing improves model accuracy and leads to higher payoffs, it also raises costs associated with data acquisition or loss of privacy, causing agents to be strategic about their data contribution. This leads to undesirable behavior at a Nash equilibrium (NE) such as free-riding, resulting in sub-optimal fairness, data sharing, and welfare. To address this, we design MSHAP, a budget-balanced payment mechanism for FL, that admits Nash equilibria under mild conditions, and achieves reciprocal fairness: where each agent's payoff equals her contribution to the collaboration, as measured by the Shapley share. In addition to fairness, we show that the NE under MSHAP has desirable guarantees in terms of accuracy, welfare, and total data collected. We validate our theoretical results through experiments, demonstrating that MSHAP outperforms baselines in terms of fairness and efficiency.