Better market Maker Algorithm to Save Impermanent Loss with High Liquidity Retention

Abstract: Decentralized exchanges (DEXs) face persistent challenges in liquidity retention and user engagement due to inefficiencies in conventional automated market maker (AMM) designs. This work proposes a dual-mechanism framework to address these limitations: a ``Better Market Maker (BMM)'', which is a liquidity-optimized AMM based on a power-law invariant ($X^nY = K$, $n = 4$), and a dynamic rebate system (DRS) for redistributing transaction fees. The segment-specific BMM reduces impermanent loss by 36\% compared to traditional constant-product ($XY = K$) models, while retaining 3.98x more liquidity during price volatility. The DRS allocates fees ($\gamma V$, $\gamma \in {0.003, 0.005, 0.01}$) with a rebate ratio $\rho \in [0.3, 0.4]$ to incentivize trader participation and maintain continuous capital injection. Simulations under high-volatility conditions demonstrate impermanent loss reductions of 36.0\% and 40\% higher user engagement compared to static fee models. By segmenting markets into high-, mid-, and low-volatility regimes, the framework achieves liquidity depth comparable to centralized exchanges (CEXs) while maintaining decentralized governance and retaining value within the cryptocurrency ecosystem.