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Register a new userI Want to Tell You? Maximizing Revenue in First-Price Two-Stage Auctions
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A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a Best and Final Offer (BAFO) stage. This final bid can depend on new information provided about either the asset or the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information settings. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer to not reveal information.
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In quasi-proportional auctions, each bidder receives a fraction of the allocation equal to the weight of their bid divided by the sum of weights of all bids, where each bids weight is determined by a weight function. We study the relationship between the weight function, bidders private values, number of bidders, and the sellers revenue in equilibrium. It has been shown that if one bidder has a much higher private value than the others, then a nearly flat weight function maximizes revenue. Essentially, threatening the bidder who has the highest valuation with having to share the allocation maximizes the revenue. We show that as bidder private values approach parity, steeper weight functions maximize revenue by making the quasi-proportional auction more like a winner-take-all auction. We also show that steeper weight functions maximize revenue as the number of bidders increases. For flatter weight functions, there is known to be a unique pure-strategy Nash equilibrium. We show that a pure-strategy Nash equilibrium also exists for steeper weight functions, and we give lower bounds for bids at an equilibrium. For a special case that includes the two-bidder auction, we show that the pure-strategy Nash equilibrium is unique, and we show how to compute the revenue at equilibrium. We also show that selecting a weight function based on private value ratios and number of bidders is necessary for a quasi-proportional auction to produce more revenue than a second-price auction.
Since 2019, most ad exchanges and sell-side platforms (SSPs), in the online advertising industry, shifted from second to first price auctions. Due to the fundamental difference between these auctions, demand-side platforms (DSPs) have had to update their bidding strategies to avoid bidding unnecessarily high and hence overpaying. Bid shading was proposed to adjust the bid price intended for second-price auctions, in order to balance cost and winning probability in a first-price auction setup. In this study, we introduce a novel deep distribution network for optimal bidding in both open (non-censored) and closed (censored) online first-price auctions. Offline and online A/B testing results show that our algorithm outperforms previous state-of-art algorithms in terms of both surplus and effective cost per action (eCPX) metrics. Furthermore, the algorithm is optimized in run-time and has been deployed into VerizonMedia DSP as production algorithm, serving hundreds of billions of bid requests per day. Online A/B test shows that advertisers ROI are improved by +2.4%, +2.4%, and +8.6% for impression based (CPM), click based (CPC), and conversion based (CPA) campaigns respectively.
We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with $n$ buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the revenue optimal mchanism, namely the Myersonian mechanism, via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar, Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than $1-1/e$ approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting.
Second-price auctions with deposits are frequently used in blockchain environments. An auction takes place on-chain: bidders deposit an amount that fully covers their bid (but possibly exceeds it) in a smart contract. The deposit is used as insurance against bidders not honoring their bid if they win. The deposit, but not the bid, is publicly observed during the bidding phase of the auction. The visibility of deposits can fundamentally change the strategic structure of the auction if bidding happens sequentially: Bidding is costly since deposit are costly to make. Thus, deposits can be used as a costly signal for a high valuation. This is the source of multiple inefficiencies: To engage in costly signalling, a bidder who bids first and has a high valuation will generally over-deposit in equilibrium, i.e.~deposit more than he will bid. If high valuations are likely there can, moreover, be entry deterrence through high deposits: a bidder who bids first can deter subsequent bidders from entering the auction. Pooling can happen in equilibrium, where bidders of different valuations deposit the same amount. The auction fails to allocate the item to the bidder with the highest valuation.
We study mechanisms for selling a single item when buyers have private values for their outside options, which they forego by participating in the mechanism. This substantially changes the revenue maximization problem. For example, the seller can strictly benefit from selling lotteries already in the single-buyer setting. We bound the menu size and the sample complexity for the optimal single-buyer mechanism. We then show that posting a single price is in fact optimal under the assumption that either (1) the outside option value is independent of the item value, and the item value distribution has decreasing marginal revenue or monotone hazard rate; or (2) the outside option value is a concave function of the item value. Moreover, when there are multiple buyers, we show that sequential posted pricing guarantees a large fraction of the optimal revenue under similar conditions.
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