Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 8: Accept
review_content: This paper draws from concepts and patterns of game theory and economics to re-interpret common machine learning algorithms, and introduces a paradigm of n-player games such that there exists a simple way to study such games where each player is individually optimized by machine learning algorithms. 

Overall, this is a very interesting and inspiring paper with its interdisciplinary touch, but at the same time doesn’t lose readability for audience with mostly machine learning background. The paper is clear, concise, and well-written, and hence I do not have any overarching comments. There are several suggestions and questions, though, that I’d like to propose.

1. Since many concepts are not from the machine learning domain, further and more detailed touch on related work are very beneficial. The current section of related work (Section 1.2) is more succinct than laying the right background information. Authors could consider giving some examples of “market mechanism”, and similarly for “design pattern”. This can give readers some ideas on how this present work’s use of “existing design pattern” is different from prior works’ proposals of “market mechanism”. Again for the second paragraph, although these concepts are more familiar to the audience, a short description for each mentioned concept is good to include (e.g. monotone games, etc)

2. Move Lemma 1 before Definition 2? Since Lemma 1 is most related to Definition 1 and not related to Definition 2.

3. For Definition 2, authors could consider adding “the classic definition [of Nash equilibrium]” to the list to clarify the difference. This classic Nash equilibrium definition will be referred to again in later sections. 

4. In Section 2.1, consider giving a formal definition of “potential game”.

5. In Section 2.3, it is not immediately clear after the text why stop_gradient becomes a problem.

6. In Section 3.1, could we elucidate a bit on what is “near zero sum”?

7. In Section 5, why the equation following the text “firm i’s forecast” is always positive? Since by definition, forecast is meant to represent the change of profit, which can be negative?

review_title: Official Blind Review #3

final_score: rating: 8: Accept
review_content: This paper introduces smooth market games (SM-games), a class of smooth games characterized by pairwise zero sum interactions, and show SM-games possess a number of appealing properties:
- A fixed point is a local Nash equilibrium iff it is stable
- Local convergence to stable fixed points
- Unstable fixed points are repellent
- Dynamics are bounded, assuming diminishing returns-to-scale for sufficiently large vectors.
The need for a class of games with such properties is motivated by a discussion of the pathologies of smooth games under simultaneous gradient ascent. 

The paper has an extensive literature review, addresses an important problem, and has informative discussions. It is well written and there are nice examples to illustrate the central ideas. However, I do have some criticisms:

1. The writing in this paper is sometimes pompous. Quoting James Scott has no added value to this work. Reference to Adam Smith’s invisible hand not only has no added value but is also confusing and detracts from the paper — SM-games are not purporting to be real economic models.
2. Throughout the paper there is a confusing mix between ideas from economics and ideas from accounting. For example, it is not correct to say that aggregate revenue is the same as GDP. Revenue is an accounting term to show how much benefit you record in a year. GDP measures the value of production. It would be more accurate to write that aggregate output and GDP are the same. But if SM-games are reflecting the perspective of an accountant, as is stated, why is GDP being discussed at all? Similarly, the idea of a dummy player with off the book costs is not consistent with an accounting perspective. I think that the paper would be clearest if it did not attempt to use terminology from other fields. But if it is going to do so, it should make a more substantial effort to do so consistently.
review_title: Official Blind Review #2

Meta-review: The paper discusses smooth market games and demonstrate the merit of the approach.    The reviewers agree on the quality of the paper, and the comments have been addressed well by the authors.

Decision: Accept (Poster)