Optimal Design of Automated Market Makers on Decentralized Exchanges

by Associate Professor Chen Yang

 

Automated market makers are a popular mechanism used on decentralized exchanges, through which users trade assets directly and automatically with each other via a liquidity pool and a fixed pricing function. The liquidity provider contributes to the liquidity pool by supplying assets to it, and in return, they earn trading fees from investors who trade within the pool. In this talk, we present a model of optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a centralized market, and consume in multiple periods. We derive the optimal strategy for the liquidity provider and the optimal design of the automated market maker that maximizes the liquidity provider's utility. We find that the optimal unit trading fee increases with the volatility of the fundamental exchange rate of the two assets, and that the optimal pricing function is chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider. Furthermore, we also study a gas-fee competition game between arbitrageurs who maximize their expected profit from trading when facing an arbitrage opportunity.