The Ad Types Problem

Colini-Baldeschi, Riccardo; Mestre, Julián; Schrijvers, Okke; Wilkens, Christopher A.

doi:10.1007/978-3-030-64946-3_4

Cited by 5 publications

(12 citation statements)

References 35 publications

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“…All missing proofs are given in the full version of the paper [9]. The extended version [9] also considers the more general Ad Types auction environment [11] in which different ads have different discount curves. It is shown that for a suitable generalization of GSP it still holds that IC-Envy ≥ IC-Regret.…”

Section: Our Contributionsmentioning

confidence: 99%

“…We look at auctions with 5 slots, where different bidders have different monotonically decreasing discount curves over the slots (cf. the Ad Types model in [9,11]). In this setting, not all ads can target all slots (as a consequence of the different discount curves, not by assumption), and the greedy allocation algorithm is no longer optimal.…”

Section: Using Envy To Predict Regretmentioning

confidence: 99%

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Envy, Regret, and Social Welfare Loss

Colini-Baldeschi

Leonardi

Schrijvers

et al. 2020

Proceedings of the Web Conference 2020

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Incentive compatibility (IC) is a desirable property for any auction mechanism, including those used in online advertising. However, in real world applications practical constraints and complex environments often result in mechanisms that lack incentive compatibility. Recently, several papers investigated the problem of deploying black-box statistical tests to determine if an auction mechanism is incentive compatible by using the notion of IC-Regret that measures the regret of a truthful bidder. Unfortunately, most of those methods are computationally intensive, since they require the execution of many counterfactual experiments.In this work, we show that similar results can be obtained using the notion of IC-Envy. The advantage of IC-Envy is its efficiency: it can be computed using only the auction's outcome. In particular, we focus on position auctions. For position auctions, we show that for a large class of pricing schemes (which includes e.g. VCG and GSP), IC-Envy ≥ IC-Regret (and IC-Envy = IC-Regret under mild supplementary conditions). Our theoretical results are completed showing that, in the position auction environment, IC-Envy can be used to bound the loss in social welfare due to the advertiser untruthful behavior.Finally, we show experimentally that IC-Envy can be used as a feature to predict IC-Regret in settings not covered by the theoretical results. In particular, using IC-Envy yields better results than training models using only price and value features.

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Section: Our Contributionsmentioning

confidence: 99%

Section: Using Envy To Predict Regretmentioning

confidence: 99%

Envy, Regret, and Social Welfare Loss

Colini-Baldeschi

Leonardi

Schrijvers

et al. 2020

Proceedings of the Web Conference 2020

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“…This paper characterizes equilibrium welfare and revenue properties of various auction formats in the Ad Types setting. The Ad Types setting [10] is a generalization of the standard position auction [11,27], which has been a workhorse in online advertising for years. In the standard position auction setting, there are multiple positions where the auctioneer can place ads.…”

Section: Introductionmentioning

confidence: 99%

“…The Ad Types setting [10] is a semi-separable generalization of position auctions where each ad has a publicly known type 1 -such as 'video ad', 'link-click ad' or 'impression ad'-and each ad type τ has its own associated position discount curve 1 ≥ δ 1 τ ≥ δ 2 τ ≥ .. ≥ 0. All ads from the same type share the same discount curve; as such, the model generalizes the position auction while maintaining more structure than a general max-weight bipartite matching problem.…”

Section: Introductionmentioning

confidence: 99%

“…Colini-Baldeschi et al [10] show that in the Ad Types setting, one can compute the optimal allocation (with respect to reported bids) and associated Vickrey-Clarke-Groves (VCG) prices using an adapted version of the Kuhn-Munkres algorithm in O(n 2 (k + log n)) (where n is the number of slots, and k the number of ad types). However, there are two practical considerations that need to be taken into account: First, despite the auction-theoretical benefits of VCG, in practice online advertising platforms often use a Generalized Second-Price (GSP) payment rule [2], so it is desirable to understand the impact of using GSP pricing instead of VCG.…”

Section: Introductionmentioning

confidence: 99%

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Equilibria in Auctions With Ad Types

Elzayn¹,

Colini-Baldeschi²,

Schrijvers³

2021

Preprint

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This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting [10]) with greedy or optimal allocation combined with generalized second-price (GSP) or Vickrey-Clarke-Groves (VCG) pricing. We make three contributions: first, we give upper and lower bounds on the Price of Anarchy (PoA) for auctions which use greedy allocation with GSP pricing, greedy allocations with VCG pricing, and optimal allocation with GSP pricing. Second, we give Bayes-Nash equilibrium characterizations for two-player, two-slot instances (for all auction formats) and show that there exists both a revenue hierarchy and revenue equivalence across some formats. Finally, we use no-regret learning algorithms and bidding data from a large online advertising platform and no-regret learning algorithms to evaluate the performance of the mechanisms under semi-realistic conditions. For welfare, we find that the optimal-to-realized welfare ratio (an empirical PoA analogue) is broadly better than our upper bounds on PoA; For revenue, we find that the hierarchy in practice may sometimes agree with simple theory, but generally appears sensitive to the underlying distribution of bidder valuations.

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