# Smooth markets: A basic mechanism for organizing gradient-based learners

arXiv: https://arxiv.org/abs/2001.04678 · HTML: https://mlsanity.com/paper/2001.04678/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Learning in Matrix Games can be Arbitrarily Complex](https://mlsanity.com/paper/2103.03405/) (2021)
- [Modularity in Reinforcement Learning via Algorithmic Independence in Credit Assignment](https://mlsanity.com/paper/2106.14993/) (2021)
- [Nash, Conley, and Computation: Impossibility and Incompleteness in Game Dynamics](https://mlsanity.com/paper/2203.14129/) (2022)

## Abstract (arXiv)

With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or controlling general n-player games. We therefore introduce smooth markets (SM-games), a class of n-player games with pairwise zero sum interactions. SM-games codify a common design pattern in machine learning that includes (some) GANs, adversarial training, and other recent algorithms. We show that SM-games are amenable to analysis and optimization using first-order methods.