Maximizing Revenue Robustly with Minimal Statistical Information

📝 Original Paper Info

- Title: Robust Revenue Maximization Under Minimal Statistical Information
- ArXiv ID: 1907.04220
- Date: 2022-04-29
- Authors: Yiannis Giannakopoulos, Diogo Po c{c}as and Alexandros Tsigonias-Dimitriadis

📝 Abstract

We study the problem of multi-dimensional revenue maximization when selling $m$ items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we assume that the seller has a very restricted knowledge of this prior: they only know the mean $\mu_j$ and an upper bound $\sigma_j$ on the standard deviation of each item's marginal distribution. Our goal is to design mechanisms that achieve good revenue against an ideal optimal auction that has full knowledge of the distribution in advance. Informally, our main contribution is a tight quantification of the interplay between the dispersity of the priors and the aforementioned robust approximation ratio. Furthermore, this can be achieved by very simple selling mechanisms. More precisely, we show that selling the items via separate price lotteries achieves an $O(\log r)$ approximation ratio where $r=\max_j(\sigma_j/\mu_j)$ is the maximum coefficient of variation across the items. To prove the result, we leverage a price lottery for the single-item case. If forced to restrict ourselves to deterministic mechanisms, this guarantee degrades to $O(r^2)$. Assuming independence of the item valuations, these ratios can be further improved by pricing the full bundle. For the case of identical means and variances, in particular, we get a guarantee of $O(\log(r/m))$ which converges to optimality as the number of items grows large. We demonstrate the optimality of the above mechanisms by providing matching lower bounds. Our tight analysis for the single-item deterministic case resolves an open gap from the work of Azar and Micali [ITCS'13]. As a by-product, we also show how one can directly use our upper bounds to improve and extend previous results related to the parametric auctions of Azar et al. [SODA'13].

💡 Summary & Analysis

The paper investigates a scenario where the seller has limited information about the buyer's valuation for multiple items in an auction setting. Specifically, the seller only knows each item’s mean value and an upper bound on its standard deviation. The research team proposed using separate price lotteries for each item to maximize revenue under these conditions. This method achieves an $O(\log r)$ approximation ratio where $r$ is the maximum coefficient of variation among items, showing that even with limited statistical information, robust revenue maximization can be achieved through simple mechanisms.

📄 Full Paper Content (ArXiv Source)

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