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

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.