# Improved Price Oracles: Constant Function Market Makers

arXiv: https://arxiv.org/abs/2003.10001 · HTML: https://mlsanity.com/paper/2003.10001/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2020.

## Built on by (most cited first, 12 of 12)

- [Explainable AI via Learning to Optimize](https://mlsanity.com/paper/2204.14174/) (2022)
- [Uniswap Liquidity Provision: An Online Learning Approach](https://mlsanity.com/paper/2302.00610/) (2023)
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- [Smart Proofs via Smart Contracts: Succinct and Informative Mathematical Derivations via Decentralized Markets](https://mlsanity.com/paper/2102.03044/) (2021)
- [QLAMMP: A Q-Learning Agent for Optimizing Fees on Automated Market Making Protocols](https://mlsanity.com/paper/2211.14977/) (2022)
- [Quantum Adaptive Self-Attention for Financial Rebalancing: An Empirical Study on Automated Market Makers in Decentralized Finance](https://mlsanity.com/paper/2509.16955/) (2025)
- [Predictive Crypto-Asset Automated Market Making Architecture for Decentralized Finance using Deep Reinforcement Learning](https://mlsanity.com/paper/2211.01346/) (2022)
- [Benchmarking Temporal Web3 Intelligence: Lessons from the FinSurvival 2025 Challenge](https://mlsanity.com/paper/2602.23159/) (2026)
- [Game of Trust: How Trustworthy Does Your Blockchain Think You Are?](https://mlsanity.com/paper/2505.14551/) (2025)
- [Reinforcement Learning for Execution under Dynamic Fees in a Closed-Loop DEX Simulator](https://mlsanity.com/paper/2607.10960/) (2026)
- [Concentrated Liquidity Provision: a Reinforcement Learning Perspective](https://mlsanity.com/paper/2608.19389/) (2026)
- [SAiFE-gym: Model-based Environments for Automated Market Making with Concentrated Liquidity](https://mlsanity.com/paper/2609.17788/) (2026)

## Abstract (arXiv)

Automated market makers, first popularized by Hanson's logarithmic market scoring rule (or LMSR) for prediction markets, have become important building blocks, called 'primitives,' for decentralized finance. A particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers (or CFMMs) which includes existing popular market makers such as Uniswap, Balancer, and Curve, whose yearly transaction volume totals to billions of dollars. We give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset and that they can do so in a computationally efficient way. We also derive several other useful properties that were previously not known. These include lower bounds on the total value of assets held by CFMMs and lower bounds guaranteeing that no agent can, by any set of trades, drain the reserves of assets held by a given CFMM.