Toxicity-Competitiveness Trade-off in Concentrated Liquidity Provision at a Decentralized Exchange

This paper investigates whether concentrated liquidity in decentralized exchanges offers liquidity providers (LPs) enhanced protection against toxic swaps by arbitrageurs while preserving efficient price discovery, focusing on Uniswap. We develop a game-theoretic model of liquidity provision that reveals a fundamental toxicity-competitiveness trade-off in LP decision-making, which shapes the equilibrium strategy. Specifically, while arbitrageurs' toxic swaps generate non-competitive payoffs that are independent of other LPs' strategies, noise traders' non-toxic swaps create competitive payoffs that depend on aggregate liquidity provision. We demonstrate that LP equilibrium payoffs under the concentrated liquidity mechanism increasingly outperform those without it as swap toxicity rises. However, when toxicity is substantially low, competitive pressure of concentrated liquidity can worsen LP payoffs. Our comparative statics analysis identifies several patterns that can guide LPs in adapting their strategies to market conditions.