Equilibrium Reward for Liquidity Providers in Automated Market Makers

ABSTRACT We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader–follower stochastic game, where the venue is the leader and a representative LP is the follower. We derive approximate closed‐form equilibrium solutions to the stochastic game and analyze the reward structure. The equilibrium strategies we find characterize the scenarios when LPs have incentives to add liquidity to the pool. The equilibrium contract depends on the external price, the pool reference price, and the pool reserves. Our framework offers insights into AMM design for maximizing order flow while ensuring LP profitability.