Maintain my current score
I’m a bit surprised by the number of positive reviews this paper has received, especially considering the following factors:
- **This paper did not use the full 9 pages.** The paper could have used the remaining 1/2 page space to add the **missing conclusion**.
- **First price pacing equilibrium has more positive structural properties than the equilibrium studied in this paper**, To further elaborate, budget pacing already guarantees there exists a pacing equilibrium and such equilibrium can be computed or even by learning algorithms efficiently. Especially considering that this paper studies the autobidders, we need to examine whether this equilibrium can be efficiently achieved, i.e., whether an equilibrium exists that can be found efficiently, and whether there is a learning dynamic such that when all bidders use it, an equilibrium can be reached. **However, this paper lacks these important analyses of the equilibrium.**
- **the gaps in the literature it cites**. The paper cites papers w.r.t pacing equilibrium only from Google but **misses a lot of important work from both academia and other companies**, i.e., [1], [2], [3], [5], [6]. **The missed citations and the paper writing give the impression that the paper’s contribution is more significant than it is**. This should be considered when assessing the overall impact of the work.
Here is my response to the author's rebuttal below.
- **Submodular / unit-demand bidders in autobidding**. [3] already studies the first price pacing for general utility, so it is possible to consider the utility model beyond additive.
- **Unconventional" liquid welfare definition.** Liquid welfare is initially (and by convention) defined when the bidder has a **budget constraint,** so the definition of liquid welfare has a max over total value a bidder could have and his own budget, please see [4] as the reference. This paper does not include a budget, which is why the reviewer still believes the liquid welfare discussed is different from the commonly used version.
- **PoA definition**. There is no formal definition of the equilibrium you've considered in this paper. This is a presentation issue.
- **Price in Section 5 depending on value:**: "this is the common assumption in the literature of algorithms / mechanisms with predictions." **Please support this argument with references**. From the reviewer's perspective, however, this reserve method cannot be applied iteratively to obtain the most efficient equilibrium due to strategic issues, see [7]. In this light, **the reserve method would have an insignificant improvement over no-reserve in practice**.
[1] Conitzer, V., Kroer, C., Panigrahi, D., Schrijvers, O., Stier-Moses, N. E., Sodomka, E., & Wilkens, C. A. (2022). Pacing equilibrium in first price auction markets. Management Science, 68(12), 8515-8535.
[2] Gao, Y., & Kroer, C. (2023). Infinite-dimensional fisher markets and tractable fair division. Operations Research, 71(2), 688-707.
[3] Feng, Y., Lucier, B., & Slivkins, A. (2024, June). Strategic Budget Selection in a Competitive Autobidding World. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing (pp. 213-224).
[4] Dobzinski, S., & Leme, R. P. (2014, July). Efficiency guarantees in auctions with budgets. In International Colloquium on Automata, Languages, and Programming (pp. 392-404). Berlin, Heidelberg: Springer Berlin Heidelberg.
[5] Lucier, B., Pattathil, S., Slivkins, A., & Zhang, M. (2024, June). Autobidders with budget and roi constraints: Efficiency, regret, and pacing dynamics. In The Thirty Seventh Annual Conference on Learning Theory (pp. 3642-3643). PMLR.
[6] Golrezaei, N., Jaillet, P., Liang, J. C. N., & Mirrokni, V. (2023, April). Pricing against a budget and roi constrained buyer. In International Conference on Artificial Intelligence and Statistics (pp. 9282-9307). PMLR.
[7] Amin, K., Rostamizadeh, A., & Syed, U. (2013). Learning prices for repeated auctions with strategic buyers. Advances in neural information processing systems, 26.