Paper:
Dynamic Revenue Sharing *
Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixedpercentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction α of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c/(1 − α) for each item, but it is not the optimal solution on maximizing the profit of the intermediary. While previous studies (by Mirrokni and Gomes, and by Niazadeh et al) focused on revenue-sharing schemes in static double auctions, in this paper, we take advantage of the repeated nature of the auctions. In particular, we introduce dynamic revenue sharing schemes where we balance the two constraints over different auctions to achieve higher profit and seller revenue. This is directly motivated by the practice of advertising exchanges where the fixed-percentage revenue-share should be met across all auctions and not in each auction. In this paper, we characterize the optimal revenue sharing scheme that satisfies both constraints in expectation. Finally, we empirically evaluate our revenue sharing scheme on real data.

Review:
This paper studies marketplaces where there is a single seller, multiple buyers, and multiple units of a single good that are sold sequentially. Moreover, there is an intermediary that sells the item for the seller. The intermediary is allowed to keep some of the revenue, subject to various constraints. The underlying auction is the second-price auction with reserve prices. The intermediary must determine how to set the reserve price in order to maximize its profit. Since this auction format is strategy-proof for the buyers, they assume the buyers bid truthfully. They also make the assumption that the seller will report its costs truthfully.
First, the authors study “single period revenue sharing,” where at every time step, the intermediary can keep at most an alpha fraction of the revenue and it must cover the seller’s reported cost if the item is sold. Next, they study “multi period revenue sharing,” where the aggregate profit of the intermediary is at most an alpha fraction of the buyers’ aggregate payment and the costs must be covered in aggregate as well. For both of these settings, the authors determine the optimal reserve price. Theoretically, the authors show that multi period revenue sharing has the potential to outperform single period revenue sharing when there are many bidders (the second-highest bid is high), and the seller’s cost is “neither too high nor too low.” They analyze several other model variants as well.
The authors experimentally compare the optimal pricing policies they come up with for the various models with the “naïve policy” which sets the reserve price at c/(1-alpha). Their experiments are on real-world data from an ad exchange. They show that the single period and multi period policies improve over the naïve policy, and the multi period policy outperforms the single period policy.
This paper studies what I think is an interesting and seemingly very applicable auction format. It’s well-written and the results are not obvious. I’d like to better understand the authors’ assumption that the seller costs are reported truthfully. The authors write, “Note that the revenue sharing contract guarantees, at least partially, when the constraint binds (which always happens in practice), the goals of the seller and the platform are completely aligned: maximizing profit is the same as maximizing revenue. Thus, sellers have little incentive to misreport their costs.” I think this means that in practice, the cost is generally so low in contrast to the revenue that the revenue sharing constraint dominates the minimum cost constraint. This doesn’t really convince me that the seller has little incentive to misreport her cost as very high to extract more money from the exchange. Also, as far as I understand, this statement detracts from the overall goal of the paper since it says that in practice, it’s always sufficient to maximize revenue, so the intermediary can ignore the sellers and can just run the Myerson auction. The application to Uber’s platform is also a bit confusing to me because Uber sets the price for the passenger and the pay for the driver. So is Uber the intermediary? The drivers seem to have no say in the matter; they do not report their costs.
=====After author feedback=====
That makes more sense, thanks.