Multiplicative Pacing Equilibria in Auction Markets

Conitzer, Vincent; Kroer, Christian; Sodomka, Eric; Stier-Moses, Nicolás E.

doi:10.48550/arxiv.1706.07151

Cited by 5 publications

(19 citation statements)

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“…Another important repeated game setting with such carryover effect is the repeated ad-auction game with limited budgets. The papers of [4,7,8] consider such games and offers results on convergence to equilibrium as well as understanding equilibria in the first-price auction settings under a particular behavioral model of the agents. Analyzing such systems for the more commonly used second-price auction system is an important open problem.…”

Section: Further Related Workmentioning

confidence: 99%

Stability and Learning in Strategic Queuing Systems

Gaitonde

Tardos

2020

Proceedings of the 21st ACM Conference on Economics and Computation

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Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. In this paper, we study this phenomenon in the context of a game modeling queuing systems: routers compete for servers, where packets that do not get service will be resent at future rounds, resulting in a system where the number of packets at each round depends on the success of the routers in the previous rounds. We model this as an (infinitely) repeated game, where the system holds a state (number of packets held by each queue) that arises from the results of the previous rounds. We assume that routers satisfy the no-regret condition, e.g. they use learning strategies to identify the server where their packets get the best service.Classical work on repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent (beyond the influence on learning from past history). The carryover effect caused by packets remaining in this system makes learning in our context result in a highly dependent random process. We analyze this random process and find that if the capacity of the servers is high enough to allow a centralized and knowledgeable scheduler to get all packets served even when service rates are halved, and queues use no-regret learning algorithms, then the expected number of packets in the queues will remain bounded throughout time, assuming older packets have priority. This paper is the first to study the effect of selfish learning in a queuing system, where the learners compete for resources, but rounds are not all independent: the number of packets to be routed at each round depends on the success of the routers in the previous rounds. CCS Concepts: • Mathematics of computing → Queueing theory; • Theory of computation → Online learning theory; Multi-agent learning; Regret bounds; Quality of equilibria; Convergence and learning in games.

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Section: Further Related Workmentioning

confidence: 99%

Stability and Learning in Strategic Queuing Systems

Gaitonde

Tardos

2020

Proceedings of the 21st ACM Conference on Economics and Computation

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“…Balseiro et al [2017Balseiro et al [ , 2020a provide a thorough study to compare di erent commonly used budget management strategies in practice. Conitzer et al [2017Conitzer et al [ , 2018 study pacing algorithms for budget constraints in both rst price auctions and second price auctions.…”

Section: Related Workmentioning

confidence: 99%

Robust Auction Design in the Auto-bidding World

Balseiro¹,

Deng²,

Mao³

et al. 2021

Preprint

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In classic auction theory, reserve prices are known to be e ective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints-a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms-and show that the introduction of reserve prices has a novel impact on the market. Namely, by choosing reserve prices appropriately the auctioneer can improve not only the total revenue but also the total welfare. Our results also demonstrate that reserve prices are robust to bidder types, i.e., reserve prices work well for di erent bidder types, such as value maximizers and utility maximizers, without using bidder type information. We generalize these results for a variety of auction mechanisms such as VCG, GSP, and rst-price auctions. Moreover, we show how to combine these results with additive boosts to improve the welfare of the outcomes of the auction further. Finally, we complement our theoretical observations with an empirical study con rming the e ectiveness of these ideas using data from online advertising auctions.

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“…the second inequality holds if inequality ( 10) is violated and the final inequality is based on the violation of inequality (11). Let event ζ t (s, ℓ, s * , ℓ * ) be n t−1 (b) = s, n t−1 (v) = ℓ, n t−1 (b * ) = s * , n t−1 (v * ) = ℓ * and by union bound, we have…”

Section: Times Then With Probability At Leastmentioning

confidence: 99%

“…Advertisers have to spend time and energy in figuring out the optimal bidding strategy for different placements, a process which can be quite costly especially when incentives differ across different publishers. For DSPs this is problematic because common budget management techniques, such as multiplicative pacing, are only optimal when the individual auctions are incentive compatible [11].…”

Section: Introductionmentioning

confidence: 99%

Online Learning for Measuring Incentive Compatibility in Ad Auctions?

Feng

Schrijvers

Sodomka

2019

The World Wide Web Conference

Self Cite

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In this paper we investigate the problem of measuring end-to-end Incentive Compatibility (IC) regret given black-box access to an auction mechanism. Our goal is to 1) compute an estimate for IC regret in an auction, 2) provide a measure of certainty around the estimate of IC regret, and 3) minimize the time it takes to arrive at an accurate estimate. We consider two main problems, with different informational assumptions: In the advertiser problem the goal is to measure IC regret for some known valuation v, while in the more general demandside platform (DSP) problem we wish to determine the worst-case IC regret over all possible valuations. The problems are naturally phrased in an online learning model and we design Regret-UCB algorithms for both problems. We give an online learning algorithm where for the advertiser problem the error of determining IC shrinks as O |B| T · ln T n + ln T n (where B is the finite set of bids, T is the number of time steps, and n is number of auctions per time step), and for the DSP problem it shrinks as O |B| T · |B| ln T n + |B| ln T n . For the DSP problem, we also consider stronger IC regret estimation and extend our Regret-UCB algorithm to achieve better IC regret error. We validate the theoretical results using simulations with Generalized Second Price (GSP) auctions, which are known to not be incentive compatible and thus have strictly positive IC regret.

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Multiplicative Pacing Equilibria in Auction Markets

Cited by 5 publications

References 0 publications

Stability and Learning in Strategic Queuing Systems

Stability and Learning in Strategic Queuing Systems

Robust Auction Design in the Auto-bidding World

Online Learning for Measuring Incentive Compatibility in Ad Auctions?

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