Equilibrium Incentives and Rewards for AMM Liquidity Providers

Summary

The document analyzes how an automated market maker can set rewards for strategic liquidity providers to encourage order flow. It models the venue as a leader that chooses a contract and a representative provider as a follower who responds, framing their interaction as a stochastic game.

The authors derive approximate closed-form equilibrium solutions and examine how the resulting contract shapes liquidity decisions. Providers are motivated to contribute liquidity when greater average pool liquidity is associated with attracting more noise trading. The reward arrangement depends on the external market price, the pool’s reference price, and its reserves. The abstract presents a theoretical framework and its implications for AMM design, but gives no empirical validation or detailed assumptions, so the conclusions should be read as model-based rather than demonstrated market outcomes.

Key ideas

• The venue chooses a reward contract while a representative liquidity provider responds strategically.
• The interaction is modeled as a leader-follower stochastic game.
• Approximate closed-form solutions are used to characterize the equilibrium contract.
• Providers contribute liquidity when deeper average liquidity is linked to increased noise trading.
• The contract depends on the external price, the pool reference price, and reserves.

Tags

# Equilibrium Reward for Liquidity Providers in Automated Market Makers


# Equilibrium Reward for Liquidity Providers in Automated Market Makers









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. Our findings suggest that under the equilibrium contract, LPs have incentives to add liquidity to the pool only when higher liquidity on average attracts more noise trading. 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.