Liquidity Fragmentation or Optimization? Analyzing Automated Market Makers Across Ethereum and Rollups

2024-10-14

AI Summary

This paper addresses the imbalance in Automated Market Maker (AMM) liquidity allocation between Ethereum’s mainnet and Rollup chains, revealing that liquidity providers (LPs) on mainnet AMMs earn annualized returns significantly below Ethereum staking yields, with no significant positive correlation between total value locked (TVL) and trading volume. Method: We first theoretically establish that AMM liquidity returns should converge to the ETH staking rate; then develop a cross-layer optimal liquidity allocation model using Lagrange multipliers, incorporating elasticity coefficient estimation and empirical validation. Contribution/Results: We propose a “rebalance–migrate–stake” three-phase optimization framework. Quantitative analysis shows that over 67% of mainnet AMM liquidity should be migrated to L2 or reallocated to staking. Empirical evaluation demonstrates that this strategy increases LPs’ expected annualized returns by more than 40%, and validates a multi-chain AMM return equilibrium convergence mechanism—providing both theoretical foundations and actionable guidelines for cross-chain liquidity governance.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Large Multimodal Models (LMMs)
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Blockchains and distributed ledgers
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Layer-2 (L2) blockchains offer security guarantees for Ethereum while reducing transaction (gas) fees. Consequently, they are gaining popularity among traders at Automated Market Makers (AMMs), but Liquidity Providers (LPs) are lagging behind. Our empirical results show that AMM liquidity pools on Ethereum are oversubscribed compared to their counterparties on L2s and deliver lower returns than staking ETH. LPs would receive higher rewards by reallocating over 2/3 of the liquidity to AMMs on L2s, or staking. We employ Lagrangian optimization to find the optimal liquidity allocation strategy that maximizes LP's rewards. Moreover, we show that the returns from liquidity provisions converge to the staking rate, and in equilibrium, liquidity provisions to any AMM should provide returns equal to staking rewards. Lastly, we measure the elasticity of trading volume with respect to TVL at AMM pools and found that at the well established blockchains an increase in TVL is not associated with an increase in trading volume.

Problem

• Ethereum
• Rollups
• Automated Market Makers

Innovation

• Optimization Strategies
• Mathematical Model for LP Allocation
• TVL and Trading Volume Nonlinear Relationship