# Approximate Nash equilibria in large nonconvex aggregative games

arXiv: https://arxiv.org/abs/2011.12604 · HTML: https://mlsanity.com/paper/2011.12604/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

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

- [Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms](https://mlsanity.com/paper/2301.08015/) (2023)
- [Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning](https://mlsanity.com/paper/2411.11793/) (2024)

## Abstract (arXiv)

This paper shows the existence of O(frac1nγ)-Nash equilibria in n-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former while γ-H"older continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with γ equal to 1, a gradient-proximal algorithm is used to construct O(frac1n)-Nash equilibria with at most O(n3) iterations. These results are applied to a numerical example concerning the demand-side management of an electricity system. The asymptotic performance of the algorithm when n tends to infinity is illustrated.