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Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations…

Formal Languages and Automata Theory · Computer Science 2023-06-22 Massimo Bartoletti , James Hsin-yu Chiang , Alberto Lluch-Lafuente

We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). We focus particularly on separability and on different invariance properties under scaling. Our main results are an axiomatic…

Computer Science and Game Theory · Computer Science 2023-02-15 Jan Christoph Schlegel , Mateusz Kwaśnicki , Akaki Mamageishvili

Dynamic-weight AMMs (aka Temporal Function Market Makers, TFMMs) implement algorithmic asset allocation, analogous to index or smart beta funds, by continuously updating pools' weights. A strategy updates target weights over time, and…

Trading and Market Microstructure · Quantitative Finance 2026-02-26 Matthew Willetts , Christian Harrington

Blockchains have popularized automated market makers (AMMs). An AMM exchange is an application running on a blockchain which maintains a pool of crypto-assets and automatically trades assets with users governed by some pricing function that…

Computer Science and Game Theory · Computer Science 2025-09-16 T-H. Hubert Chan , Ke Wu , Elaine Shi

The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some…

Computer Science and Game Theory · Computer Science 2024-02-15 Michael J. Curry , Zhou Fan , David C. Parkes

Automated Market Makers (AMMs) are used to provide liquidity for combinatorial prediction markets that would otherwise be too thinly traded. They offer both buy and sell prices for any of the doubly exponential many possible securities that…

Computer Science and Game Theory · Computer Science 2025-10-16 Maneesha Papireddygari , Xintong Wang , Bo Waggoner , David M. Pennock

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies…

Optimization and Control · Mathematics 2021-07-28 Guillermo Angeris , Akshay Agrawal , Alex Evans , Tarun Chitra , Stephen Boyd

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…

Trading and Market Microstructure · Quantitative Finance 2024-05-21 Yongge Wang

This paper presents a general framework for the design and analysis of exchange mechanisms between two assets that unifies and enables comparisons between the two dominant paradigms for exchange, constant function market markers (CFMMs) and…

Functional Analysis · Mathematics 2023-04-21 Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden

Liquidity providers (LPs) are essential figures in the operation of automated market makers (AMMs); in exchange for transaction fees, LPs lend the liquidity that allows AMMs to operate. While many prior works have studied the incentive…

Computer Science and Game Theory · Computer Science 2025-09-22 Bruno Llacer Trotti , Weizhao Tang , Rachid El-Azouzi , Giulia Fanti , Daniel Sadoc Menasche

Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We…

Computer Science and Game Theory · Computer Science 2023-04-10 Rafael Frongillo , Maneesha Papireddygari , Bo Waggoner

Designing automated market makers (AMMs) for prediction markets on combinatorial securities over large outcome spaces poses significant computational challenges. Prior research has primarily focused on combinatorial prediction markets…

Computer Science and Game Theory · Computer Science 2024-11-15 Prommy Sultana Hossain , Xintong Wang , Fang-Yi Yu

Decentralized Finance (DeFi) has revolutionized financial markets by enabling complex asset-exchange protocols without trusted intermediaries. Automated Market Makers (AMMs) are a central component of DeFi, providing the core functionality…

Mathematical Finance · Quantitative Finance 2026-02-03 Marco Dessalvi , Massimo Bartoletti , Alberto Lluch-Lafuente

Automated Market Makers (AMMs) are a class of smart contracts on Ethereum and other blockchains that "make markets" autonomously. In other words, AMMs stand ready to trade with other market participants that interact with them, at the…

Mathematical Finance · Quantitative Finance 2022-12-22 Stefan Loesch

This paper conducts an empirical investigation into the effects of Designated Market Makers (DMMs) on key market quality indicators, such as liquidity, bid-ask spreads, and order fulfillment ratios. Through agent-based simulations, this…

Trading and Market Microstructure · Quantitative Finance 2024-09-26 Cong Zhou

Automated Market Makers (AMMs) are essential to decentralized finance, offering continuous liquidity and enabling intermediary-free trading on blockchains. However, participants in AMMs are vulnerable to Maximal Extractable Value (MEV)…

Computer Science and Game Theory · Computer Science 2024-10-25 Mengqian Zhang , Sen Yang , Fan Zhang

Automated Market Makers (AMMs) are a cornerstone of decentralized finance. They are smart contracts (stateful programs) running on blockchains. They enable virtual token exchange: traders swap tokens with the AMM for a fee, while liquidity…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-03 Hongyin Chen , Amit Vaisman , Ittay Eyal

We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if…

Trading and Market Microstructure · Quantitative Finance 2021-07-22 Agostino Capponi , Ruizhe Jia

We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model…

Mathematical Finance · Quantitative Finance 2026-04-14 Cheuk Yin Lee , Shen-Ning Tung , Tai-Ho Wang

In this paper, we describe a novel agent-based approach for modelling the transaction cost of buying or selling an asset in financial markets, e.g., to liquidate a large position as a result of a margin call to meet financial obligations.…

Trading and Market Microstructure · Quantitative Finance 2025-05-22 Perukrishnen Vytelingum , Rory Baggott , Namid Stillman , Jianfei Zhang , Dingqiu Zhu , Tao Chen , Justin Lyon