# Distributed Nash Equilibrium Seeking by A Consensus Based Approach

arXiv: https://arxiv.org/abs/1602.00771 · HTML: https://mlsanity.com/paper/1602.00771/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2016.

## Built on by (most cited first, 8 of 8)

- [The Hidden Strength of Disagreement: Unraveling the Consensus-Diversity Tradeoff in Adaptive Multi-Agent Systems](https://mlsanity.com/paper/2502.16565/) (2025)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Learning to Control Unknown Strongly Monotone Games](https://mlsanity.com/paper/2407.00575/) (2024)
- [Learning equilibria with personalized incentives in a class of nonmonotone games](https://mlsanity.com/paper/2111.03854/) (2021)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [Distributed Differentiable Dynamic Game for Multi-robot Coordination](https://mlsanity.com/paper/2207.08892/) (2022)
- [Diffusion Stochastic Learning Over Adaptive Competing Networks](https://mlsanity.com/paper/2504.19635/) (2025)
- [Choose Your Battles: Distributed Learning Over Multiple Tug of War Games](https://mlsanity.com/paper/2509.20147/) (2025)

## Abstract (arXiv)

In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the non-cooperative games. Analytical analysis on the convergence of the players' actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with non-quadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a non-local convergence result for the non-quadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players' actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy.