# Optimal Automated Market Makers: Differentiable Economics and Strong Duality

arXiv: https://arxiv.org/abs/2402.09129 · HTML: https://mlsanity.com/paper/2402.09129/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [Complexity of Mechanism Design](https://mlsanity.com/paper/1408.1486/) (2014)
- [Automated Mechanism Design via Neural Networks](https://mlsanity.com/paper/1805.03382/) (2018)
- [A Permutation-Equivariant Neural Network Architecture For Auction Design](https://mlsanity.com/paper/2003.01497/) (2020)
- [Auction learning as a two-player game](https://mlsanity.com/paper/2006.05684/) (2020)
- [Sample Complexity of Automated Mechanism Design](https://mlsanity.com/paper/1606.04145/) (2016)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [Certifying Strategyproof Auction Networks](https://mlsanity.com/paper/2006.08742/) (2020)
- [Strong Duality for a Multiple-Good Monopolist](https://mlsanity.com/paper/1409.4150/) (2014)
- [Duality and Optimality of Auctions for Uniform Distributions](https://mlsanity.com/paper/1404.2329/) (2014)
- [Automated Market Making and Loss-Versus-Rebalancing](https://mlsanity.com/paper/2208.06046/) (2022)
- [Optimal Auctions with Restricted Allocations](https://mlsanity.com/paper/1606.01610/) (2016)
- [Estimating Approximate Incentive Compatibility](https://mlsanity.com/paper/1902.09413/) (2019)
- [Mechanism Design via Optimal Transport](https://mlsanity.com/paper/1503.01958/) (2015)
- [A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers](https://mlsanity.com/paper/2303.00208/) (2023)
- [An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets](https://mlsanity.com/paper/2302.00196/) (2023)
- [Mode Connectivity in Auction Design](https://mlsanity.com/paper/2305.11005/) (2023)
- [An Axiomatic Study of Scoring Rule Markets](https://mlsanity.com/paper/1709.10065/) (2017)
- [Replicating Market Makers](https://mlsanity.com/paper/2103.14769/) (2021)
- [Finding the Right Curve: Optimal Design of Constant Function Market Makers](https://mlsanity.com/paper/2212.03340/) (2022)
- [Arbitrage-Free Combinatorial Market Making via Integer Programming](https://mlsanity.com/paper/1606.02825/) (2016)

## Built on by (most cited first, 1 of 1)

- [Learning Truthful Mechanisms without Discretization](https://mlsanity.com/paper/2506.22911/) (2025)

## Abstract (arXiv)

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 predetermined schedule; the best choice of this schedule depends on the market maker's goals. The literature on the design of AMMs has mainly focused on prediction markets with the goal of information elicitation. More recent work motivated by DeFi has focused instead on the goal of profit maximization, but considering only a single type of good (traded with a numeraire), including under adverse selection (Milionis et al. 2022). Optimal market making in the presence of multiple goods, including the possibility of complex bundling behavior, is not well understood. In this paper, we show that finding an optimal market maker is dual to an optimal transport problem, with specific geometric constraints on the transport plan in the dual. We show that optimal mechanisms for multiple goods and under adverse selection can take advantage of bundling, both improved prices for bundled purchases and sales as well as sometimes accepting payment "in kind." We present conjectures of optimal mechanisms in additional settings which show further complex behavior. From a methodological perspective, we make essential use of the tools of differentiable economics to generate conjectures of optimal mechanisms, and give a proof-of-concept for the use of such tools in guiding theoretical investigations.