Real-time Bidding for Time Constrained Impression Contracts in First and Second Price Auctions - Theory and Algorithms

We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.

Multi-armed bandits for bid shading in first-price real-time bidding auctions

Online advertisements are bought through a mechanism called real-time bidding (RTB). In RTB, the ads are auctioned in real-time on every webpage load. The ad auctions can be of two types: second-price or first-price auctions. In second-price auctions, the bidder with the highest bid wins the auction, but they only pay the second-highest bid. This paper focuses on first-price auctions, where the buyer pays the amount that they bid. This research evaluates how multi-armed bandit strategies optimize the bid size in a commercial demand-side platform (DSP) that buys inventory through ad exchanges. First, we analyze seven multi-armed bandit algorithms on two different offline real datasets gathered from real second-price auctions. Then, we test and compare the performance of three algorithms in a production environment. Our results show that real data from second-price auctions can be used successfully to model first-price auctions. Moreover, we found that the trained multi-armed bandit algorithms reduce the bidding costs considerably compared to the baseline (naïve approach) on average 29%and optimize the whole budget by slightly reducing the win rate (on average 7.7%). Our findings, tested in a real scenario, show a clear and substantial economic benefit for ad buyers using DSPs.

EXPRESS: First-Price Auctions in Online Display Advertising

We link the rapid and dramatic move from second-price to first-price auction format in the display advertising market to the move from the waterfalling mechanism employed by publishers for soliciting bids in a pre-ordered cascade over exchanges, to an alternate header bidding strategy that broadcasts the request for bid to all exchanges simultaneously. First, we argue that the move by the publishers from waterfalling to header bidding was a revenue improving move for publishers in the old regime when exchanges employed second-price auctions. Given the publisher move to header bidding, we show that exchanges move from second-price to first-price auctions to increase their expected clearing prices. Interestingly, when all exchanges move to first-price auctions, each exchange faces stronger competition from other exchanges and some exchanges may end up with lower revenue than when all exchanges use second-price auctions; yet, all exchanges move to first-price auctions in the unique equilibrium of the game. We show that the new regime hinders the exchanges’ ability to differentiate in equilibrium. Furthermore, it allows the publishers to achieve the revenue of the optimal mechanism despite not having direct access to the advertisers.

Fairness and Efficiency in Online Advertising Mechanisms

Online advertising often involves targeting ads to certain types of consumers where ads are commonly sold by generalized second price auctions. However, such an auction or mechanism could be considered unfair if similar consumers are consistently shown different ads or consistently receive different payoffs. Results show that such ascending bid auctions may result in unfair treatment and additionally that uncertainty regarding an ad’s value can result in inefficiency. An alternative way to assign ads to consumers is presented called the random assignment mechanism. Results show that the random assignment can improve fairness while improving efficiency in some circumstances.

Linear Program-Based Approximation for Personalized Reserve Prices

We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the [Formula: see text]-approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP.