# Games played by Exponential Weights Algorithms

arXiv: https://arxiv.org/abs/2407.06676 · HTML: https://mlsanity.com/paper/2407.06676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 2 of 2)

- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos](https://mlsanity.com/paper/1703.01138/) (2017)

## Abstract (arXiv)

This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm characterized by an initial mixed action and a fixed learning rate, so that the mixed action profile pt played at stage t follows an homogeneous Markov chain. At first, we show that whenever a strict Nash equilibrium exists, the probability to play a strict Nash equilibrium at the next stage converges almost surely to 0 or 1. Secondly, we show that the limit of pt, whenever it exists, belongs to the set of ``Nash Equilibria with Equalizing Payoffs''. Thirdly, we show that in strong coordination games, where the payoff of a player is positive on the diagonal and 0 elsewhere, pt converges almost surely to one of the strict Nash equilibria. We conclude with open questions.