Paper: Decongestion by Representation: Learning to Improve Economic Welfare in Marketplaces (ICLR-2024)

Reviewer comment (Theory):
The theoretical analysis feels a little misplaced. Specifically, the theoretical analysis seems to focus on the perfect information equilibrium, is this really relevant in the online marketplace scenario as the authors note earlier in the paper? Furthermore, this focuses on proxying social welfare with reducing congestion but this may not be the objective platforms want to optimize for. In fact, decongestion seems practical enough objective on its own. This also involves making assumptions like "item heterogeneity is captured in revealed features" which is likely violated in practice.

Author response:
**”The theoretical analysis seems to focus on the perfect information equilibrium, is this really relevant in the online marketplace scenario as the authors note earlier in the paper?”**  
Please note that CE prices do not imply “perfect” (or complete) information, and the theory of market equilibrium is generally silent as to how equilibrium prices arise. Rather, this is conceptualized as an adjustment (or `tatonnement’) process whereby prices settle down to values wherein supply balances demand or with sellers becoming informed through participation in other markets. By these means, equilibrium prices emerge - irrespective of informational considerations. In our settings, we emphasize the fact that the learning platform *does not* observe consumer values; in fact, this is precisely the reason why prices are useful within our proxy objective, providing an alternative to these unobserved values.

**“Decongestion seems practical enough objective on its own.”**   
Please note that in general, decongestion is in itself insufficient: any solution in which users choose differently - or do not choose at all - leads to zero congestion, but can be arbitrarily bad. The notion of monotonicity (page 6) provides a sufficient condition for when increasing the number of allocations (e.g., by decongestion) also improves welfare.

Reviewer comment (Writing):
In Abstract “The power of a platform is limited to controlling representations—the subset of information about items presented by default to users”. This statement is very strong and seems not true. For instance, platforms definitely have other means to control information: besides representations (the amount of info provided per item) there are different ways to control user attention between different items like ranking of items, recommendation of items, etc. So, I strongly suggest rewriting this sentence.

Author response:
Thank you for this suggestion. We agree and already make this point later in the introduction (4th paragraph). We will make sure this message is also conveyed in the abstract.

Reviewer comment (Novelty):
In Intro, the end of 2nd paragraph and 3rd paragraph: I do not understand why the described issue cannot be resolved by some auction (or other mechanism design). The way these paragraphs are written, it sounds like the authors are not aware of vast practical application of auction in web services, e.g., ad auctions, where they are built to reduce congestion by maximizing welfare (e.g., second price auctions, position auctions) through exploiting imbalance between demand and supply; and in this case, prices (bids) are also set in a decentralized way – so, this argument does not imply a strong conclusion that representation is the only way.

Author response:
Thank you for this comment, please let us clarify: We agree that the general problem of optimizing welfare admits many possible approaches (auctions being one of them). True, if we were to design a *new* platform, or allowed to drastically change a current platform’s market mechanism, then an alternative would be to implement an auction mechanism - or even have the platform itself set prices. 

However, our work asks: how can a platform that *already* operates a market with seller-mediated prices improve welfare? We argue that *given this setup* - which is very common - it is inevitable that there is a choice to make about item representation, and that this provides an unexplored degree of freedom through which a platform can improve welfare. Thus, the “inevitability” we discuss concerns the *informational* aspect - not the overall market design choice. We will clarify this. 

Our choice to focus on platforms that operate “conventional” price-based (and seller-mediated price based) markets stems from their popularity: consider Airbnb, Zillow, Etsy, Upwork, AliExpress, Wayfair, and many others - all of which are consumer-facing and deal with complex products or services that must match with complex consumer preferences. And while auctions may be common for other domains (e.g., ads), they are far less so for consumer-facing platforms (Ebay is perhaps the only exception, and it too enables direct price setting be sellers).

Reviewer comment (Theory):
In Intro, Page 2, 3rd paragraph: “under perceived values remain both valuable and diverse.” Why? The example after this does not help and is unclear. Why cannot the problem be resolved by auctions (so that the platform adjusts price despite its decentralized price input) or by ranking (playing with user attention)?

Author response:
Thank you for this comment, please let us clarify: We agree that the general problem of optimizing welfare admits many possible approaches (auctions being one of them). True, if we were to design a *new* platform, or allowed to drastically change a current platform’s market mechanism, then an alternative would be to implement an auction mechanism - or even have the platform itself set prices. 

However, our work asks: how can a platform that *already* operates a market with seller-mediated prices improve welfare? We argue that *given this setup* - which is very common - it is inevitable that there is a choice to make about item representation, and that this provides an unexplored degree of freedom through which a platform can improve welfare. Thus, the “inevitability” we discuss concerns the *informational* aspect - not the overall market design choice. We will clarify this. 

Our choice to focus on platforms that operate “conventional” price-based (and seller-mediated price based) markets stems from their popularity: consider Airbnb, Zillow, Etsy, Upwork, AliExpress, Wayfair, and many others - all of which are consumer-facing and deal with complex products or services that must match with complex consumer preferences. And while auctions may be common for other domains (e.g., ads), they are far less so for consumer-facing platforms (Ebay is perhaps the only exception, and it too enables direct price setting be sellers).

Reviewer comment (Novelty):
The argumentation of the viability of the proposed setup should be reviewed and rewritten: the setup itself sounds reasonable, but it should not be positioned as the only way to resolve the marketplace/platform issues.

Author response:
Thank you for this comment, please let us clarify: We agree that the general problem of optimizing welfare admits many possible approaches (auctions being one of them). True, if we were to design a *new* platform, or allowed to drastically change a current platform’s market mechanism, then an alternative would be to implement an auction mechanism - or even have the platform itself set prices. 

However, our work asks: how can a platform that *already* operates a market with seller-mediated prices improve welfare? We argue that *given this setup* - which is very common - it is inevitable that there is a choice to make about item representation, and that this provides an unexplored degree of freedom through which a platform can improve welfare. Thus, the “inevitability” we discuss concerns the *informational* aspect - not the overall market design choice. We will clarify this. 

Our choice to focus on platforms that operate “conventional” price-based (and seller-mediated price based) markets stems from their popularity: consider Airbnb, Zillow, Etsy, Upwork, AliExpress, Wayfair, and many others - all of which are consumer-facing and deal with complex products or services that must match with complex consumer preferences. And while auctions may be common for other domains (e.g., ads), they are far less so for consumer-facing platforms (Ebay is perhaps the only exception, and it too enables direct price setting be sellers).

Reviewer comment (Writing):
The Introduction can have more details while preserving the same space. For instance, while reading the whole Introduction, it was still unclear what is meant by “representation”: whether representation is dependent on item (in Setup it is found it is not), whether it is about something like ranking or not (in Setup it is found it is not).

Author response:
Thank you for your comment. We will make clear the precise meaning of representation in the introduction (as you note, this is formally defined in Sec. 2).

Reviewer comment (Writing):
The term “welfare” is ambiguous. Is it just about users? Or users + platform? Or users + sellers? Only in Setup is it found to be about users only, BUT in Intro it is written “reduced social welfare—to the detriment of users, suppliers, and the platform itself” which is misleading.

Author response:
We work with the standard definition of social welfare, is which is the sum of utility to consumers *plus* the sum of revenue to sellers. A consumer’s utility is the value of the allocated item minus its price. The revenue to a seller is the price of the item sold. Because payments are transferred from buyers to sellers, these terms cancel out in the total sum:

$W = \sum_i \sum_j a_{ij} (v_{ij} - p_j) + \sum_j \sum_i a_{ij} p_j = \sum_i \sum_j a_{ij} v_{ij},$

which is precisely Eq. (3). We will clarify this in the final revision.

Hence, welfare does consider utility to both buyers and sellers, while being agnostic to the way in which utility is distributed across different participants. We adopt welfare to users as the goal of the platform and this reflects a platform that is motivated by long-term engagement and satisfaction of users (and will seek to gain a share of transaction volume through transaction fees and/or other indirect forms of monetization).

Reviewer comment (Experiments):
Section 4 could include some practical examples where these conditions are working.

Author response:
The strongest condition (in Proposition 1) applies to markets in which the absolute differences in valuations (across items and users) is small relative to the magnitude of values. For example, consider a set of apartments in a certain location and of similar size, whose prices may differ due to different characteristics (such as layout or precise location), but where these differences are minor relative to apartments’ generally large `base’ price.

The other conditions (1-5) aim to capture more subtle aspects of how the different characteristics behave. In particular, when does the representation of a limited number of features maintain efficient choices by users? In the apartments example, if all of the apartments in the market have similar, average-sized windows (condition 1), or if all users attribute sufficiently low value to the feature “has curtains” (condition 2), then an optimal allocation can be supported even while dropping these features in the item representation.

Reviewer comment (Novelty):
In Intro, Page 2, 2nd paragraph: “Given this, we propose to use machine learning to solve the necessary design problem of choosing beneficial item representations.” Is it true that ML usage is a separate contribution in addition to the proposed setup? Or is ML a part of the setup? It would be beneficial to have a clear list of the contributions.

Author response:
Yes, we believe that our setup and our approach (which is ML-based) are distinct contributions - the former conceptual, and the latter practical. In principle, we agree that one could attempt to solve Eq. (3) by employing some discrete optimization algorithm directly over masks, and without training or using a predictive model of user choice. However, this would not make use of readily-available past market data, and is a challenging bi-level combinatorial optimization problem even for a single market (Eq. (3)).

Reviewer comment (Theory):
Equation (6) and (7): Is it acceptable to train both f on S and use the same S for W_S calculation? Should S be split? Despite theoretical analysis of non-ML setup in Section 4, there are no guarantees on viability of the proposed ML approach (are we using standard ML setting with well-known theory and practice?). It would be nice to have such a discussion somewhere in the text.

Author response:
Yes - we do not see a reason why this approach is not sound.

Reviewer comment (Writing):
How are V_{het} and V_{hom} formally defined?

Author response:
Please see Appendix D for a detailed description.

Reviewer comment (Reproducibility):
It would be nice to have a formal direct link/reference to the Appendix where details of experimentation are given (both for Section 5.1 and for Section 5.2). This is important for reproducibility.

Author response:
Complete experimental details are given in Appendix D (for Sec. 5.1) and Appendix E (for Sec. 5.2). We will note this in the main text.

Reviewer comment (Writing):
In Section 5.2: “we optimize Eq.(8) using Adam with…”. What is “Adam”? It is better to give a reference/citation, or a clearer naming.

Author response:
Adam is a highly-popular gradient-based optimization method due to Kingma and Ba (2014). Thank you for this suggestion, we will add an appropriate citation.

Reviewer comment (Theory):
Equation (7) notation: formally, it is incorrect to write M ∈ S since S consists of pairs (M, y). This should be replaced by (M,y) ∈ S or by a sum over l = 1,…,L.

Author response:
This is true, we will fix this in the next revision.

Reviewer comment (Theory):
The core of the optimization technique is to replace the welfare function with a lower bound proxy. I'm curious how tight Eq (5) is? It would be nice to add some discussions in this regard.

Author response:
**Is Eq. 5 tight?**   
Generally, our proxy welfare objective need not be tight, which is expected given that it does not include unobserved valuations (whereas true welfare does). One case in which our proxy is tight is when preferences are fully heterogeneous and prices are seller-optimal CE. These conditions ensure that term (II) in Eq. (4) is zero (i.e., there is no congestion) and term (I) aligns with welfare. This is analogous to proxy losses for classification: hinge loss and log-loss are useful as proxies to 0-1 loss and exact in simple special cases (e.g., separability).