reviews: 
Comments: The paper introduces a new decoding strategy for LM's based on a game theoretic formulation. It is directed at tasks requiring objective, factual answers for which a clear notion of a generative version and a discriminative version can be applied. In such settings, the paper describes an adaptation of recent regularized equilibrium approaches that operate directly on the outputs of samples from the Generator/discriminator to produce final answers that do quite well in experiments over a range of challenging fact-seeking or reasoning-seeking benchmarks.
Strengths: Originality: There have a lot of recent investigations into improved decoding strategies; this paper's approach is quite original in taking a game-theoretic formulation to (essentially) the problem of factuality from language models. This actually makes a lot of sense; human language as pointed out in one of the references is a strategic game between agents and thus we should be modeling it as such and not a pure optimization problem. This particular insight is not new, but this idea stands out to me because of its practicality. It should be noted that the idea could be said to be inspired by recent work on diplomacy and the core algorithm is an adaptation of the same. However, it takes a good deal of originality to make the connection to discriminator/generator as a game and present the particular formulation in the paper.

Quality: The approach has the strong benefit of simplicity in implementation, it requires no re-training of the LM itself. It does seem to require some degree of non-trivial post-processing in the form of running the iteration procedure of eq 1/2. The authors dont address this but I would expect that it would not affect overall latency of LM inference by much and also it scales zero with LM size (iiuc). The experimental evaluation is quite exhaustive and satisfactory, there are a range of datset types explored. the equilibrium methods don't dominate on every single dataset but they generally do quite close to the SoTA and in some instances far exceed. 

Clarity: The motivational sections, the presentation of the key insight and the experimental section are mostly quite clear and the paper was a pleasure to read. I appreciate the use of shading to visualize the relative improvement between the best and other methods in Table 1/2/3.

Significance: I think this could be an very impactful paper. The results are generally very good, it is easy to implement and does not require extensive tuning it seems to get to work, and it seems from my understanding to be scalable to very large LM sizes.
Weaknesses: Clarity: The paper is actually written fairly well, but there could be some improvements: 
 a. sec 2.2 was far too short. readers without any Game theory background might not even know what regret means. You dont need to fully flesh out all the derivation and algorithm, but a better intuition I think should be built, which might require 2-3 paragaphs more. I think this can be taken from the experimental section, where although there is a lot of useful material, at a pinch some of it can be moved to appendix to make room. Further a couple of (minor) sources of confusion on my first read:

 a.  'reasonableness' is a bit of a misleading word for the concept you are trying to capture. Maybe 'alignment' ? bu that has other implications in the LM space.
 b. eq 1/2: i think it's helpful to clarify that this update does not result in a backprop to the params of the LM. The reason is that in the current RLHF literature that is generally what happens so it is easy to get confused.
 
c. Bit confusing to put ER-G and ER-D in the section on "Baselines".


Quality: I am not at all sure about the characterization of SC as significantly related to Contrastive Decoding. The idea of using a weaker LM as the contrastive seems quite significant to me as it enables the strong LM to "avoid" the weaker ones mistakes, which for reasoning problems often are systematic reasoning errors. So it is unfortunate that CD was not compared against (Though I guess the paper with strong results for CD on reasoning problems was quite recent?) 

Significance:  The biggest challenge to the potential significance of this work is that it doesnt seem readily applicable for all use cases of LMs. You need a sort of fact-checking problem, where a set of candidate answers are present. This means it can't be used out of the box as a general decoder, which would be sort of a holy grail right now. Nevertheless, I think the set of applications it is relevant for is hugely important and it is likely to find application given its ease of use.
Recommendation: 10: strong accept, should be highlighted at the conference
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: 4 excellent
Clarity: 3 good