# Continuous-Time Convergence Rates in Potential and Monotone Games

arXiv: https://arxiv.org/abs/2011.10682 · HTML: https://mlsanity.com/paper/2011.10682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2020.

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

- [Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting](https://mlsanity.com/paper/2111.09982/) (2021)

## Abstract (arXiv)

In this paper, we provide exponential rates of convergence to the interior Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in N-player continuous concave games that satisfy certain monotonicity assumptions while possibly also admitting potential functions. In the first part of this paper, we provide a novel relative characterization of monotone games and show that MD and its discounted version converge with O(e-β t) in relatively strongly and relatively hypo-monotone games, respectively. In the second part of this paper, we specialize our results to games that admit a relatively strongly concave potential and show AC converges with O(e-β t). These rates extend their known convergence conditions. Simulations are performed which empirically back up our results.