# On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information

arXiv: https://arxiv.org/abs/2005.06923 · HTML: https://mlsanity.com/paper/2005.06923/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2020.

## Built on by (most cited first, 3 of 3)

- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Competing Adaptive Networks](https://mlsanity.com/paper/2103.15664/) (2021)
- [Diffusion Stochastic Learning Over Adaptive Competing Networks](https://mlsanity.com/paper/2504.19635/) (2025)

## Abstract (arXiv)

This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a group of agents. A cluster is viewed as a virtual noncooperative player that aims to minimize its local payoff function and the agents in a cluster are the actual players that cooperate within the cluster to optimize the payoff function of the cluster through communication via a connected graph. In our setting, agents have only partial-decision information, that is, they only know local information and cannot have full access to opponents' decisions. To solve the NE seeking problem of this formulated game, a discrete-time distributed algorithm, called distributed gradient tracking algorithm (DGT), is devised based on the inter- and intra-communication of clusters. In the designed algorithm, each agent is equipped with strategy variables including its own strategy and estimates of other clusters' strategies. With the help of a weighted Fronbenius norm and a weighted Euclidean norm, theoretical analysis is presented to rigorously show the linear convergence of the algorithm. Finally, a numerical example is given to illustrate the proposed algorithm.