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Equilibrium Reward for Liquidity Providers in Automated Market Makers

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arxiv 2503.22502 v1 pith:ZT2LLFTB submitted 2025-03-28 q-fin.TR math.OC

Alif Aqsha , Philippe Bergault , Leandro Sánchez-Betancourt This is my paper · ORCID
classification q-fin.TRmath.OC
keywords equilibriumliquiditycontractorderpoolautomatedflowgame
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strategic Analysis of Just-In-Time Liquidity Provision in Concentrated Liquidity Market Makers

    cs.GT 2025-09 conditional novelty 7.0 of 10

    A transaction-level optimization model shows that JIT liquidity providers on Uniswap V3 could raise profits by up to 69% by accounting for price impact, but optimized JIT activity would cut passive LP fee income by up...

  2. Optimal Fees for Liquidity Provision in Automated Market Makers

    q-fin.TR 2025-08 conditional novelty 7.0 of 10

    Optimal AMM fees sit just below all-in CEX trading costs in normal markets, rise with volatility, and become effectively infinite (halt trading) in extreme volatility.

  3. Competition and Incentives in a Shared Order Book

    q-fin.TR 2025-09 reject novelty 6.0 of 10

    In a two-exchange shared order book model, incentive provision by one exchange improves liquidity for both, creating a free-rider problem that the paper claims can eliminate incentives entirely.

  4. Optimal Dynamic Fees in Automated Market Makers

    q-fin.TR 2025-06 conditional novelty 6.0 of 10

    In a constant-function market maker, optimal dynamic fees balance arbitrage deterrence against noise-trader attraction, and a fee that is linear in inventory and external price is a near-optimal approximation.

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