reviews: 
Comments: The paper introduces generative adversarial equilibrium solvers (GAES), a GAN that learns to map pseudo-games to their generalized Nash equilibria from a sample of problem instances. In particular, they provide a formulation that makes the problem amenable to standard stochastic first-order methods. They use GAES to compute in a scalable way competitive equilibria in exchange economies and an environmental economic model of the Kyoto mechanism, outperforming earlier methods.
Strengths: Pseudo-games are very general game-theoretic models with a number of applications, most notably Arrow-Debreu competitive economies. Yet, there is a lack of scalable techniques for computing generalized Nash equilibria in such settings. This paper makes a concrete contribution in that direction by providing a method with promising performance across a number of benchmarks. The proposed method is natural and the experimental results are overall convincing and quite thorough. Indeed, the paper appears to attain state of the art performance in a number of important applications, and could have significant impact in this area.
Weaknesses: There are some soundness issues that the authors have to address. First, there appears to be a significant gap between the theoretical analysis and the experimental settings. Specifically, it is not clear how a stationary point in the sense of Theorem 4.1 translates to a GNE. If stationary points are not necessarily GNE, the narrative of the paper has to be restructured. In particular, it is often claimed that the method maps pseudo-games to GNE, and it is not clear whether that claim is theoretically sound. Of course, computing GNE is intractable, but it is alluded (for example in the abstract) that under a distribution over problem instances the problem could be easier. Theorem 4.1 also makes a strong concavity assumption which appears to be violated in all settings of interest. It should be the case that a "small" regularizer can always be incorporated without affecting the equilibria by much, but I think this should be discussed in more detail. 

I am also confused about Footnote 4. It is claimed that the method obtains the state of the art $O(1/\epsilon^3)$ complexity, a major improvement over $O(1/\epsilon^6)$, which the authors claim was the previous state of the art. The authors have to explain more precisely the class of problems this applies to; there are many variants of the PL condition studied in the literature. In particular, the following papers seem to obtain a much better dependency: "Faster single-loop algorithms for minimax optimization without strong concavity," "faster stochastic algoritms for minimax optimization under Polyak-Lojasiewicz Conditions" and "Doubly smoothed GDA for constrained nonconvex-nonconcave minimax optimization."

Besides the issues above, the algorithmic approach is very close to the paper "Exploitability minimization in games and beyond," which limits to some extent the algorithmic contribution of the present paper. The authors have to highlight the comparisons in more detail.
Recommendation: 6: marginally above the acceptance threshold
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 2 fair
Clarity: 3 good