Generalized Nash Equilibria: Algorithms and Limits

Generalized Nash equilibrium (GNE) problems arise naturally in multi-agent systems with coupled constraints, such as energy markets, net- worked control, and resource allocation. While recent advances have established efficient algorithms under strong monotonicity or shared constraints, many prac- tically relevant GNEs fall outside this regime. In this talk, we present a unified perspective on learning and computing GNEs drawing on some recent results.

We first discuss convergence rate guarantees for variational GNE learning in strongly monotone games with linear coupling constraints, establishing explicit rates under first-order and payoff-based information settings. We then turn to non-monotone quadratic games with individual equality constraints, where we show that the GNE conditions can be reformulated as a convex optimization problem whose objective satisfies a Polyak–Lojasiewicz (PL) condition. 

The talk will be concluded by a discussion on fundamental challenges in GNE computa- tion beyond the variational and monotone setting. 

We outline open questions related to stability, equilibrium selection, and algorithmic design in such settings, and discuss directions toward identifying additional structural propertiesthat may enable provable convergence guarantees for broader classes of GNE problems.

Join at imt.lu/sagrestia