# Geometric Convergence of Distributed Gradient Play in Games with Unconstrained Action Sets

arXiv: https://arxiv.org/abs/1907.07144 · HTML: https://mlsanity.com/paper/1907.07144/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Competing Adaptive Networks](https://mlsanity.com/paper/2103.15664/) (2021)
- [Distributed Differentiable Dynamic Game for Multi-robot Coordination](https://mlsanity.com/paper/2207.08892/) (2022)

## Abstract (arXiv)

We provide a distributed algorithm to learn a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings and unconstrained action sets. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We consider a distributed communication-based gradient algorithm. For this procedure, we prove geometric convergence to a Nash equilibrium. In contrast to our previous works [15], [16], where the proposed algorithms required two parameters to be set up and the analysis was based on a so called augmented game mapping, the procedure in this work corresponds to a standard distributed gradient play and, thus, only one constant step size parameter needs to be chosen appropriately to guarantee fast convergence to a game solution. Moreover, we provide a rigorous comparison between the convergence rate of the proposed distributed gradient play and the rate of the GRANE algorithm presented in [15]. It allows us to demonstrate that the distributed gradient play outperforms the GRANE in terms of convergence speed.