  Automated market makers (AMMs) have emerged as the dominant market mechanism
for trading on decentralized exchanges implemented on blockchains. This paper
presents a single mechanism that targets two important unsolved problems for
AMMs: reducing losses to informed orderflow, and maximizing revenue from
uninformed orderflow. The ``auction-managed AMM'' works by running a
censorship-resistant onchain auction for the right to temporarily act as ``pool
manager'' for a constant-product AMM. The pool manager sets the swap fee rate
on the pool, and also receives the accrued fees from swaps. The pool manager
can exclusively capture some arbitrage by trading against the pool in response
to small price movements, and also can set swap fees incorporating price
sensitivity of retail orderflow and adapting to changing market conditions,
with the benefits from both ultimately accruing to liquidity providers.
Liquidity providers can enter and exit the pool freely in response to changing
rent, though they must pay a small fee on withdrawal. We prove that under
certain assumptions, this AMM should have higher liquidity in equilibrium than
any standard, fixed-fee AMM.
