We study the stability of data exchange among competing firms. Unlike tangible goods, data is non-rival: sharing it does not deprive the giver of its use. On one hand, competing firms-- often operating as machine-learning-driven predictors that collect observations from a shared environment to solve similar tasks-- can improve their predictive accuracies from pooling data. On the other hand, they compete for market share, which may depend on their relative predictive performance. This raises the central question of this paper: can there be a stable data exchange in such competitive environments? We formalize this via a model of $n$ firms exchanging fractions of their datasets, with predictive performance feeding into market competition. We adopt core stability as our solution concept, accounting for externalities via worst-case responses by non-participating firms. Our main results reveal a sharp contrast driven by demand structure: (i) in fully rational markets, where customers flock entirely to the top-performing firm, a core-stable exchange always exists for any monotone continuous prediction functions; (ii) in partially rational markets with logit-style demand, core-stable exchanges may fail to exist-and even approximate cores can be empty. Our impossibility results suggest that internal profit-sharing within coalitions can restore stability in partially rational markets. We formalize this intuition by showing that when co-operating coalitions equally redistribute market-share revenues among members, a core-stable data exchange exists. Finally, we propose a natural exchange dynamic and demonstrate empirically that it converges to a core-stable data exchange in fully rational markets on simulated instances derived from real datasets.

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