Arbitrageurs' profits, LVR, and sandwich attacks: batch trading as an AMM design response
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We consider an automated market maker (AMM) in which all trades are batched and executed at a price equal to the marginal price (i.e., the price of an arbitrarily small trade) after the batch trades. We show that such an AMM is a function maximizing AMM (or FM-AMM): for given prices, it trades to reach the highest possible value of a given function. Competition between arbitrageurs guarantees that an FM-AMM always trades at a fair, equilibrium price, and arbitrage profits (also known as LVR) are eliminated. Sandwich attacks are also eliminated because all trades occur at the exogenously-determined equilibrium price. We use Binance price data to simulate the lower bound to the return of providing liquidity to an FM-AMM. We show that this bound is very close to the empirical returns of providing liquidity on Uniswap v3 (at least for the token pairs and the period we consider).
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