Abstract
This paper compares mathematical models for automated market makers (AMM) including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based AMMs. This paper proposes and analyzes constant ellipse based cost functions for AMMs. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have certain advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against slippage based front running attacks. In addition to the theoretical advantages of constant ellipse based cost functions, our implementation shows that if the model is used as a cryptographic property swap tool over Ethereum blockchain, it saves up to 46.88% gas cost against Uniswap V2 and saves up to 184.29% gas cost against Uniswap V3 which has been launched in April 2021. The source codes related to this paper are available at https://github.com/coinswapapp and the prototype of the proposed AMM is available at http://coinswapapp.io/.
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Wang, Y. (2023). Prediction Markets, Automated Market Makers, and Decentralized Finance (DeFi). In: Pardalos, P., Kotsireas, I., Guo, Y., Knottenbelt, W. (eds) Mathematical Research for Blockchain Economy. MARBLE 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-18679-0_12
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