Extend am-AMM beyond constant-product pools, particularly to concentrated liquidity AMMs

Extend the auction-managed AMM (am-AMM) mechanism beyond constant-product automated market makers to other AMM designs, particularly to concentrated liquidity AMMs in which different liquidity providers may have different returns during the same period and positions may go in or out of range as prices change.

Background

The paper introduces the auction-managed AMM (am-AMM), which uses a Harberger lease auction to select a pool manager who sets fees (subject to a cap) and captures fee revenue, with LPs receiving rent. The theoretical results and mechanism design are developed for constant-product AMMs.

The authors note that many real-world AMMs, such as Uniswap v3, use concentrated liquidity, where LP returns vary with price range occupancy. Extending the am-AMM to concentrated liquidity settings would need to address heterogeneity in LP returns, range in/out dynamics, and fair rent allocation across ranges while preserving censorship-resistance and accessibility.