Fairness and Strategy-Proofness in Automated Market Makers

Battle Count: 82

Directly relevant to DeFi market making and AMM protocol design. The impossibility theorem explains why no deployed AMM lets LPs vote on trading functions, which is fundamental to understanding current DeFi market structure. The weighted Aitchison centroid provides a concrete design formula for fair aggregation. However, the paper is purely theoretical with no empirical trading strategies, no backtesting, and no direct algorithmic trading applications. Most relevant to protocol designers and DeFi researchers rather than traditional quantitative traders. The two-asset case (where the impossibility dissolves) covers the bulk of deployed AMM volume (~$3B/day vs ~$100M/day for multi-asset).

The theoretical results are mathematically sophisticated (Cauchy functional equations, Aitchison geometry, cocycle arguments) but the practical implications are straightforward: the weighted Aitchison centroid formula (1) is a simple weighted geometric mean computation. The Moulin generalized median at n=2 is also simple to implement. The main complexity is in the proof machinery, not in applying the results. A protocol designer would need to implement the centroid formula and choose a weighting function w(V), which is computationally trivial.

Pure theoretical paper with complete formal proofs. All axioms, definitions, theorems, and proofs are self-contained. The Cauchy functional equation solution, cocycle arguments, and manipulation constructions are fully specified. No empirical data or code required. Logical independence of axioms verified in Appendix A. Extensions to general welfare objects in Appendix C.