# The Computation of Approximate Generalized Feedback Nash Equilibria

arXiv: https://arxiv.org/abs/2101.02900 · HTML: https://mlsanity.com/paper/2101.02900/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2021.

## Built on by (most cited first, 7 of 7)

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- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts](https://mlsanity.com/paper/2109.01178/) (2021)
- [Robust Forecasting for Robotic Control: A Game-Theoretic Approach](https://mlsanity.com/paper/2209.10802/) (2022)
- [Who Plays First? Optimizing the Order of Play in Stackelberg Games with Many Robots](https://mlsanity.com/paper/2402.09246/) (2024)
- [PACE: A Framework for Learning and Control in Linear Incomplete-Information Differential Games](https://mlsanity.com/paper/2504.17128/) (2025)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)

## Abstract (arXiv)

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and sufficient conditions for (local) GFNE solutions at the trajectory level, which enable the development of efficient numerical methods for their computation. Specifically, we propose a Newton-style method for finding game trajectories which satisfy necessary conditions for an equilibrium, which can then be checked against sufficiency conditions. We show that the evaluation of the necessary conditions in general requires computing a series of nested, implicitly-defined derivatives, which quickly becomes intractable. To this end, we introduce an approximation to the necessary conditions which is amenable to efficient evaluation, and in turn, computation of solutions. We term the solutions to the approximate necessary conditions Generalized Feedback Quasi-Nash Equilibria (GFQNE), and we introduce numerical methods for their computation. In particular, we develop a Sequential Linear-Quadratic Game approach, in which a LQ local approximation of the game is solved at each iteration. The development of this method relies on the ability to compute a GFNE to inequality- and equality-constrained LQ games, and therefore specific methods for the solution of these special cases are developed in detail. We demonstrate the effectiveness of the proposed solution approach on a dynamic game arising in an autonomous driving application.