# Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games

arXiv: https://arxiv.org/abs/1912.03460 · HTML: https://mlsanity.com/paper/1912.03460/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2019.

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

- [Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chains](https://mlsanity.com/paper/2201.12224/) (2022)
- [Decentralized and Uncoordinated Learning of Stable Matchings: A Game-Theoretic Approach](https://mlsanity.com/paper/2407.21294/) (2024)
- [Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting](https://mlsanity.com/paper/2111.09982/) (2021)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)

## Abstract (arXiv)

In this paper, we consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent-type dynamics. We introduce two classes of dynamics whereby the associated mirror map is constructed based on a strongly convex or a Legendre regularizer. Depending on the properties of the regularizer we show that these new dynamics can converge asymptotically in concave games with monotone (negative) pseudo-gradient. Furthermore, we show that when the regularizer enjoys strong convexity, the resulting dynamics can converge even in games with hypo-monotone (negative) pseudo-gradient, which corresponds to a shortage of monotonicity.