Trading orbits of two-asset AMMs are level sets of weighted geometric means x^w y^{1-w} derived from validity invariance, Pareto efficiency, and unit invariance.
An Axiomatic Characteriza- tion of CFMMs and Equivalence to Prediction Markets
2 Pith papers cite this work. Polarity classification is still indexing.
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For weighted-product AMMs with n≥3 assets, no aggregation rule satisfies both Arrovian fairness and strategy-proofness except single-provider dictators; the obstruction vanishes at n=2 and transfers to logarithmic opinion pools.
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From Swap Axioms to Weighted Geometric Means: A Characterization of AMMs
Trading orbits of two-asset AMMs are level sets of weighted geometric means x^w y^{1-w} derived from validity invariance, Pareto efficiency, and unit invariance.
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Fairness and Strategy-Proofness in Automated Market Makers
For weighted-product AMMs with n≥3 assets, no aggregation rule satisfies both Arrovian fairness and strategy-proofness except single-provider dictators; the obstruction vanishes at n=2 and transfers to logarithmic opinion pools.