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Main Author:	Wang, Yongge
Format:	Preprint
Published:	2020
Subjects:	Trading and Market Microstructure Discrete Mathematics Computer Science and Game Theory 91B26, 91Bxx, G.2.1; K.4.4; I.6.3; J.4
Online Access:	https://arxiv.org/abs/2009.01676
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author	Wang, Yongge
author_facet	Wang, Yongge
contents	This paper compares mathematical models for automated market makers 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 automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.
format	Preprint
id	arxiv_https___arxiv_org_abs_2009_01676
institution	arXiv
publishDate	2020
record_format	arxiv
spellingShingle	Automated Market Makers for Decentralized Finance (DeFi) Wang, Yongge Trading and Market Microstructure Discrete Mathematics Computer Science and Game Theory 91B26, 91Bxx, G.2.1; K.4.4; I.6.3; J.4 This paper compares mathematical models for automated market makers 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 automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.
title	Automated Market Makers for Decentralized Finance (DeFi)
topic	Trading and Market Microstructure Discrete Mathematics Computer Science and Game Theory 91B26, 91Bxx, G.2.1; K.4.4; I.6.3; J.4
url	https://arxiv.org/abs/2009.01676

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