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The compression of high-dimensional data is a central problem in information theory, traditionally dominated by two paradigms: compression for signal reconstruction — as in lossless or lossy coding — and ​compression for utility — as in feature leaning to preserve the latent information. Here, we introduce and formalize a third, largely unexplored paradigm: compression for competition and incentivization. Unlike its predecessors, this approach aims not to preserve the intrinsic content of data but rather its relational integrity, ensuring that a desired ranking or preorder among data points is maintained after compression.