Strategic Bonding Curves in Automated Market Makers

The bonding curves of decentralized exchanges (DEXs) define with mathematical formulae the relationship between liquidity supply and prices. Most DEXs use the bonding curves of constant function markets (CFMs) to clear the supply and demand of liquidity. At present, liquidity providers (LPs) operate at a loss in CFMs on average. We generalize CFMs and introduce decentralized liquidity pools (DLPs), which provide LPs with the tools to design dynamic bonding curves according to strategic preferences. In DLPs, impact functions encode how orders affect prices, and quote functions determine the price of liquidity. To illustrate the strategic flexibility of DLPs, we develop models for bonding curves when prices form across multiple venues, within the DLP, or in a competing venue. In fragmented markets, the DLP estimates the fundamental price from the trading flow to adjust the bonding curve and reduce arbitrage losses. Our models may be used as hooks in Uniswap v4 when the DLP’s impact functions are the constant product function.