Toxicity-Competitiveness Trade-off in Concentrated Liquidity Provision

Decentralized exchanges (DEXs) adopt automated market makers (AMM) as an alternative to the traditional limit-order book (LOB), which is too costly to implement with blockchain technology. To protect liquidity providers (LPs) against toxic trades by arbitrageurs, Uniswap v3, the leading DEX, has introduced a concentrated liquidity mechanism that allows LPs to restrict the price range accepting trades. We define a liquidity provision game of this setting and characterize the optimal strategy and equilibrium liquidity allocation. We demonstrate that LP profits consist of the competitive and non-competitive parts. Crucially, the non-competitive components arise from toxic trades by arbitrageurs. Consequently, liquidity provision involves a toxicity-competitiveness tradeoff as opposed to the literature understanding them as two independent factors. By incorporating this tradeoff, we derive a novel guideline and implications for liquidity provision in the decentralized financial market.