# Stochastic Multiplicative Weights Updates in Zero-Sum Games

arXiv: https://arxiv.org/abs/2110.02134 · HTML: https://mlsanity.com/paper/2110.02134/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2021.

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

- [Auctions Between Regret-Minimizing Agents](https://mlsanity.com/paper/2110.11855/) (2021)
- [How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agents](https://mlsanity.com/paper/2112.07640/) (2021)
- [Learnable Mixed Nash Equilibria are Collectively Rational](https://mlsanity.com/paper/2510.14907/) (2025)
- [Multi-agent learning under uncertainty: Recurrence vs. concentration](https://mlsanity.com/paper/2512.08132/) (2025)

## Abstract (arXiv)

We study agents competing against each other in a repeated network zero-sum game while applying the multiplicative weights update (MWU) algorithm with fixed learning rates. In our implementation, agents select their strategies probabilistically in each iteration and update their weights/strategies using the realized vector payoff of all strategies, i.e., stochastic MWU with full information. We show that the system results in an irreducible Markov chain where agent strategies diverge from the set of Nash equilibria. Further, we show that agents will play pure strategies with probability 1 in the limit.