Posted Price Programmatic Guarantee in Display Advertising
arXiv:1708.01348v1 [cs.GT] 4 Aug 2017
Bowei Chen† ∗, Jingmin Huang† , Yufei Huang‡ , Stefanos Kollias† , Shigang Yue† † School of Computer Science, University of Lincoln, UK ‡ School of Management, University of Bath, UK
1
Abstract
auction-based, thus has achieved a significant automation, integration and user-targeting [19].
This paper presents a revenue maximisation model for sales channel allocation based on dynamic programming. It helps the media seller to determine how to distribute the sales volume of page views between guaranteed and nonguaranteed channels for display advertising. The model can algorithmically allocate and price the future page views via standardised guaranteed contracts in addition to real-time bidding (RTB). This is one of a few studies that investigates programmatic guarantee (PG) with posted prices. Several assumptions are made for media buyers’ behaviour, such as risk-aversion, stochastic demand arrivals, and time and price effects. We examine our model with an RTB dataset and find it increases the seller’s expected total revenue by adopting different pricing and allocation strategies depending the level of competition in RTB campaigns. The insights from this research can increase the allocative efficiency of the current media sellers’ sales mechanism and thus improve their revenue.
Guaranteed contracts have a longer tradition than RTB. In 1994, wire.com signed fourteen contracts with companies like AT&T, Club Med and Coor’z Zima, being recognised as the start of display advertising [8]. A guaranteed contract is essentially an agreement between a buyer and a seller. It is usually negotiated privately. Only a small portion of impressions is sold through guaranteed contracts but they bring in much more revenue than RTB [9]. In order to meet the demand of automation for the huge number of site visits, standardised guaranteed contracts have been recently discussed. This is known as programmatic guarantee (PG) (also called programmatic reserved, or programmatic upfront). PG is a sales system that sells future impressions via standardised guaranteed contracts in addition to RTB [15]. Examples include Google DoubleClick’s Programmatic Guaranteed, AOL’s Programmatic Upfront, Rubicon Project’s Reserved Premium Media Buys, etc. Recent studies have investigated PG from different perspectives, such as [2, 4, 6, 7, 11, 17]. The main challenges lie in the following questions: (1) How many future impressions should be allocated to standardised guaranteed contracts? (2) How much to charge for those guaranteed contracts? (3) Should the guaranteed prices be posted or not?
Introduction
In display advertising, page views (also called impressions) are mainly sold by media sellers (e.g., publishers or supplyside platforms) through two channels – being sold in advance via guaranteed contracts or being auctioned off in real time. The former is called guaranteed delivery and the latter is called RTB. Over the past several years, RTB has become to be the most popular sales model for display advertising, in which media buyers (e.g., advertisers or demand-side platforms) come to a common marketplace such as ad exchange to compete for impressions from their targeted users [13]. It is real-time, impression-level and ∗
Corresponding author:
[email protected]
This paper discusses a revenue maximisation model for posted price PG. For a specific ad slot (or user tag), the estimated total impressions in a future period can be priced and allocated algorithmically between the guaranteed market and the spot market. Impressions in the former are sold in advance via standardised guaranteed contracts until the delivery day while the latter are auctioned off in RTB. Unlike the traditional way of selling guaranteed contracts, there is no negotiation process between the buyer and the seller. The guaranteed per-impression price will be posted in a common marketplace. Media buyers can monitor the price changes over time and purchase the needed impressions directly at the corresponding prices a few days, weeks or months earlier before the delivery day. Based on auction theory and operations research studies, several
assumptions are made for media buyers’ behaviour, such as risk-aversion, stochastic demand arrivals, and time and price effects. The proposed model is examined with an RTB dataset. Our experiments show it increases the seller’s expected total revenue by adopting different pricing and allocation strategies depending the level of competition in RTB campaigns. The rest of the paper is structured as follows: Section 2 reviews the related work; Section 3 introduces our model; Section 4 presents experimental results; and Section 5 concludes the paper.
problem is how to deal with both allocation and pricing – how many future impressions to sell in advance and at what prices to sell at a specific time point? The seller’s expected total revenue consists of the expected revenue from selling the guaranteed impressions and the expected revenue from auctioning the remaining impressions in RTB. The challenge is that the pre-sold impressions changes the future supply and demand in RTB, in turn leads to the changes in the expected RTB revenue. 3.1
Revenue Maximisation Problem
The seller’s revenue optimisation can be expressed as:
2
Related Work
max R = RP G + RRT B , p
An assignment algorithm was proposed in [10] to fulfil guaranteed contracts in display advertising. Each media buyer has a contract for a certain number of impressions and each impression has a set of weighted edges to buyers. The algorithm assigns the requested impressions to each buyer and maximises the total weight of edges. In [11], the media seller was assumed to be a bidder who bids for guaranteed contracts. Impressions are allocated to auctions only if other buyers’ bids are high enough. In [2], stochastic control theory was employed to derive an optimal policy for allocating impressions to guaranteed contracts. However, the effects of allocation on ad auctions were not discussed explicitly in this work. In [6] and [17], two dynamic models were proposed and both studies discuss the scenario of accepting buy requests. In [3], a lightweight and scalable allocation framework for guaranteed contracts was proposed. It ensures the delivery of promised impressions to each contract when the total number of impressions and pre-sold guaranteed contracts are given. A similar revenue maximisation model was discussed in [7] where the guaranteed contracts have posted prices but the demand is assumed to be deterministic. Two pricing methods for guaranteed contracts were discussed in [4] based on the expected user visits and historical contracts bookings, but the allocation of impressions was not discussed.
3
Model
Our model is set as the following. Given an ad slot of a media seller, impressions that will be created from this ad slot in a future period can be sold in advance through guaranteed contracts. For simplicity and without loss of generality, guaranteed impressions are sold individually so each guaranteed contract contains a single impression. This setting can be easily extended to a bulk sale in practice. Let [T, Te] denote the future period that impressions will be created and [0, T ] be the selling period of guaranteed impressions. Suppose that the total supply and demand of impressions in the future period are well estimated, denoted by S and Q, respectively. The seller’s revenue management
subject to 0 ≤ p(tn ) ≤ Φ(tn ), for n = 0, · · · , N, N X
0≤
θ(tn , p(tn ))η(tn ) ≤ S.
(1) (2) (3)
n=0
In the objective function, RP G is the expected revenue from selling guaranteed impressions in advance, RRT B is the expected revenue from auctioning the remaining impressions in the future RTB, p = [p(t0 ), · · · , p(tN )] is a vector of guaranteed prices over equally spaced discrete time points t0 , · · · , tN , where t0 = 0 and tN = T . The future RTB period can be further denoted by [tN , tN +ς ], where ς = d T1 (Te − T )N e and d·e is the ceiling function. Eq. (2) specifies boundaries of the guaranteed price at each time point and Eq. (3) makes sure that the total amount of sold guaranteed impressions does not exceed the estimated total supply S in order to avoid over-selling problem. The expected revenue of selling guaranteed impressions in advance can be expressed as: RP G =
N X
(1 − ω$)p(tn )θ(tn , p(tn ))η(tn ),
(4)
n=0
where ω is the probability that the seller fails to deliver a guaranteed impression, $ is the size of penalty – the seller needs to pay kp(tn ) penalty if she fails to deliver a guaranteed impression that is sold at p(tn ), η(tn ) is the total (accumulative) arrived but unfilled demand at time tn and θ(tn , p(tn )) is the proportion of demand who wants to buy an impression in advance at time tn and at price p(tn ). Our demand assumptions are further discussed in Section 3.2. The expected revenue of auctioning the remaining impressions in RTB can be expressed as: N X RRT B = S − θ(tn , p(tn ))η(tn ) φ(ξ(tN )),
(5)
n=0
where ξ(tN ) is the per-auction competition level at time tN . It can be measured by the average number of media
buyers in an RTB auction. Given time tn , n = 1, · · · , N , ξ(tn ) can be obtained by examining the remaining expected supply and demand in the future, that is Pn Q − i=0 θ(ti , p(ti ))η(ti ) Pn . (6) ξ(tn ) = S − i=0 θ(ti , p(ti ))η(ti )
SP auction [14]. In other words, media buyers are truthtelling in RTB. Let ξ be the average number of buyers in an RTB campaign, the expected auction revenue can be obtained as follow: Z ξ−2 φ(ξ) = xξ(ξ − 1)g(x) 1 − F (x) F (x) dx, Ω(x)
Before presenting our solution to the optimisation problem, below we first discuss our key assumptions and settings. 3.2
Demand Assumptions
Several mild assumptions on demand are imposed. First, the demand of buying in advance is assumed to follow a homogeneous Poisson process with intensity λ. It simulates the amount of media buyers who would like to purchase in advance when there is no price effect. Let ∆t = tn − tn−1 and f (tn ) be the expected number of demand arrivals in the period [tn−1 , tn ], so f (tn ) = λ∆t. Once a demand arrives, it will last up to time tN if not fulfilled. So the cumulative expected total number of demand up to time tN should be equal to or less than Q, implying λ ≤ Q/T . Second, time and price are considered as the key factors in determining the demand of buying a guaranteed contract. As discussed earlier, the ratio function θ(t, p) represents the proportion of those who want to buy an impression in advance at time t with price p. The following conditions should hold: ∗
∗
θ(t, p) ≥ θ(t, p ), for 0 ≤ p ≤ p , 0 ≤ t ≤ T,
(7)
θ(t, p) ≥ θ(τ, p), for 0 ≤ τ ≤ t ≤ T, 0 ≤ p,
(8)
θ(t, 0) = 1, for 0 ≤ t ≤ T.
(9)
Given time tn , θ(tn , p(tn )) can be formulated as: θ(tn , p(tn )) = e−αp(tn )(1+β(tN −tn )) ,
(10)
where α represents the price effect and β represents the time effect. This functional form was firstly proposed to model the customers’ purchase behaviour in online flight bookings [1], and was also used in our previous PG research [7]. Therefore, the demand for buying a guaranteed contract at time tn can be computed as: n−1 X
η(tn ) = I{n>0}
i=0
|
f (ti )
n−1 Y
1 − θ(tj , p(tj )) +f (tn ).
j=i
{z
Remaining demand from previous time
} (11)
3.3
RTB-Based Terminal Value
In RTB, impressions are usually sold separately through seal-bid second price (SP). With private values, it is a weakly dominant strategy to bid one’s value in a seal-bid
(12) where x is a media buyer’s bid, Ω(x) is the range of bid value, g(·) and F (·) are the density and cumulative distribution functions, respectively. Therefore, the term ξ(ξ − 1)g(x)(1 − F (x))(F (x))ξ−2 represents the probability that if a media buyer who bids at x is the second highest bidder, then one of ξ − 1 other buyers must bid at least as much as she does and all of ξ − 2 other buyers have to bid no more than she does. φ(·) can be obtained from Eq. (12) as in auction theory, uniform and log-normal distributions are the popular choices for modelling the bid distribution [16, 14]. However, both distributions are not empirically on many instances [6, 7, 18]. In this paper, φ(·) will be learnt from data and detailed discussion is given in Section 4.2. 3.4
Time-Dependent Risk Preference
Given time tn , the censored upper bound Φ(tn ) for the guaranteed price p(tn ) is defined as follows: Φ(tn ) = min{φ(ξ(tn )) + δ(tn )ψ(ξ(tn )), π}, {z } |
(13)
:=χ(tn ,ξ(tn ))
where δ(tn ) is the risk preference at time tn , π is the expected maximum value, and φ(ξ(tn )) and ψ(ξ(tn )) are the expected payment and risk level of an impression from RTB for the given competition level ξ(tn ), respectively. Thus, χ(tn , ξ(tn )) represents the risk-aware upper bound of the guaranteed price at time tn . Similar to φ(·), the estimation of φ(·), ψ(·), π are given in Section 4.2. It should be noted that δ(t) satisfies the following conditions: lim δ(t) = 0, lim δ(t) = 1, δ(t)0 ≤ 0.
t→T
t→0
They make sure that a media buyer’s decision making at time tn is indifferent to PG and RTB because the guaranteed price converges to the expected payment in RTB based on the updated supply and demand levels. There are many choices of δ(·), we here simply consider an exponential decay function 1.96 × e−tn . 3.5
Solution
The problem formulated in Eq. (1) is similar to the Knapsack problem [12], where the optimisation deals with the a sequence of items with values and non-negative weights.
Algorithm 1 O PT R 1: Input: α, β, ζ, η, ω, κ, λ, S, Q, T, N 2: for n ← 0, · · · , NP do n 3: un ← min{S, i=0 f (ti )}; 4: ln ← ln−1 I{n>0} ; 5: yn ← [ln , · · · , un ]; 6: for j ← 1, · · · , |yn | do 7: H(tn , yn,j ) ← O PT H; . Algorithm 2 8: if n = N then Q−yn,j ; 9: Rj ← H(tn , yn,j )+(S −yn,j )φ S−yn,j 10: end if 11: end for 12: end for 13: Output: R∗ ← max{Rj }; Algorithm 2 O PT H 1: Input: α, β, ζ, η, ω, κ, λ, tn , yn,j 2: zn,j ← an allocation matrix with size (yn,j + 1) × 2; . Initialisation 3: for k ← 1, · · · , (yn,j + 1) do 4: pn,j,k ← Eq. (14); 5: Φn,j,k ← Eq. (12); 6: if pn,j,k > Φn,j,k then . Check price bound 7: Continue; 8: end if 9: G(tn , zn,j (k, 1)) ← pn,j,k zn,j (k, 2); e k (tn , yn,j ) ← I{n>0} H(tn−1 , zn,j (k, 2)) + 10: H G(tn , zn,j (k, 2)); 11: end for e k (tn , yn,j )}; 12: Output: H(tn , yn,j ) ← maxk {H
In our problem, prices are affected by allocation and they are further censored based on media buyers’ purchase behaviour. The expected total revenue can be divided into RP G and RRT B . When the remaining total supply and demand are given, RRT B can be estimated. So the optimal RP G can be identified using the recurrence structure of dynamic programming. Our solution is presented in Algorithm 1. The demand of guaranteed buying arrives following a homogeneous Poisson process. Together with Eq. (3), the upper bound un of total amount P of sold impressions up to time n tn can be defined by min{S, i=0 f (ti )}. Its lower bound ln is given from time tn−1 . The possible sold impressions up to time tn can then be generated, denoted by vector yn . For yn,j ∈ yn , j = 1, · · · , |yn |, its optimal subset-sum can be computed by creating an (yn,j + 1) × 2 matrix z, which contains all possible combinations of impressions sold up to time tn−1 and at time tn , such that zn,j (k, 1) + zn,j (k, 2) = yn,j , for k = 1, · · · , (yn,j + 1), and zn,j (k, 1) = 0 if n = 0.
Since zn,j (k, 2) ∝ θ(tn , p(tn )) Pn−1 ∗ i=0 f (ti ) − i=0 sj (ti )
Pn
= e−αp(tn )(1+β(tN −tn )) , Pn−1 where i=0 s∗j (ti ) is the total optimal impressions sold Pn−1 up to time tn−1 , subject to the condition i=0 s∗j (ti ) = zn,j (k, 1). It should be noted that the optimal selling amount at each step has been stored. The guaranteed price at time tn is then nP o Pn−1 ∗ n ln{zn,j (k, 1)} − ln i=0 f (ti ) − i=0 sj (ti ) pn,j,k = − . α(1 + β(tN − tn )) (14) Then Φn,j,k can be obtained by Eq. (12). If pn,j,k > Φn,j,k , pn,j,k will be censored to Φn,j,k but this solution will be removed from the solution space. At time tN , the optimal solution can then be obtained. The time complexity of the proposed solution is O(N S 2 ). Normally, N S, the algorithm is relatively scalable and efficient.
4
Experiments
This section describes our dataset, experimental settings, estimation of parameters and results of model performance. 4.1
Data
An RTB dataset from an UK supply-side provider is used in experiments to validate the proposed model. This dataset has also been used in [7, 18, 6]. It covers RTB campaigns of 31 ad slots over the period from 08 January 2013 to 14 February 2013. It should be noted that all bids are quoted in terms of cost-per-mille (CPM), which is the measurement corresponds to the value of 1000 impressions [19]. 4.2
Setting and Estimating Parameters
We select 7 days (the minimum continuous period) campaign records for all slots because the RTB campaign records range from 7 to 20 days in the sample. Given an ad slot, a delivery day (i.e., [T, Te]) is randomly selected and the campaigns reported from this day is used as the test set. The previous 6 days data of the delivery day is used as the training set to estimate model parameters. For those slots with only 7 days data, the 7th day is set to be the delivery day. In experiments, the guaranteed contracts selling period is 31 days prior to the delivery day. The total supply and demand of impressions in the delivery day are well forecast by the media seller, so Q and S are given by the test set. They can be predicted using regression models, such as the locally weighted regression scatterplot smoothing (LOWESS) model and the polynomial surface regression model, which were investigated in [7, 6] for the same
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Figure 1: Q, S, and ξ in the RTB dataset (excluding 5 ad slots whose average ξ in the training set is less 2). Group Number of ad slots Payment Winning bid ξ Payment to winning bid
1 6 0.97 (0.17) 1.13 (0.15) 8.87 (4.52) 88.85% (15.12%)
2 20 0.69 (0.59) 2.24 (0.88) 3.27 (1.75) 30.53% (17.95%)
Table 1: Clustering of 26 ad slots based on the training set. Numbers in round brackets are standard deviations. dataset. Fig. 1 summarises the total supply and demand of impressions for training and test data of 26 ad slots. 5 slots are excluded because their average competition level ξ in the training data is less than 2. It appears the total supply levels are similar across slots while the total demand levels are significantly different. It is worth noting that, within a day, ξ significantly deviates from its mean as many buyers join RTB at peak hours from 6am to 10am, in which period ξ is 118.96% higher than other hours.
χ(t, ξ(t)) for a given competition level ξ, where LOWESS, polynomial regression, and sigmod methods are used. There first two methods were discussed in estimating the total supply and demand. The sigmod method is mainly using a scaled sigmod function to approximate the training data, where the scaling parameters are calibrated based on root mean squared errors (RMSEs) [5]. We use LOWESS in experiments as it has better fitting results.
Based on ξ, the total 26 ad slots are further clustered into 2 groups using the k-means clustering method [5]. Table 1 presents a brief summary of the major statistics for 2 groups. Group 1 has average 8.87 buyers in each RTB auction, much higher than that of Group 2. Consistent with Eq. (12), the average per auction payment/revenue of Group 1 is higher than Group 2. Surprisingly, the latter has a higher average winning bid. By further investigating the distributions of winning bids and payment prices, we find that the counter-intuitive result is due to different patterns over two groups. Figs. 2-3 exhibit examples from adslot3 and adslot8, respectively. For adslot3, the distributions of winning bids and payment prices are bell shaped like Gaussian, and payment price has a higher peak and a slightly smaller mean value. For adslot8, the distributions of winning bids and payment prices are two bell shaped like Gaussian mixture, and payment prices are much less than winning bids. Table 1 also provides the ratio of payment to winning bid for 2 groups: Group 1 is with 88.85% while Group 2 is with 30.53%. The findings suggest that ad slots with lower competition level in RTB campaigns have greater potential to be optimised.
4.3
Fig. 4 shows an example of estimating φ(ξ), ϕ(ξ) and
Results
Two examples of optimal allocation and pricing of the proposed model are presented in Figs. 5-6. In a competitive market (e.g., adslot3 in Group 1), the guaranteed price surges to approximate the censored upper bound as it approaches the delivery period. Therefore, more buyers are willing to accept the contract, and the optimal allocation is around 70%. If a slot has a lower competition level in RTB campaigns (e.g., adslot8 in Group 2), the guaranteed price increases quickly and approximates the censored upper bound. Since the price is high, only a few buyers would accept the contract resulting that the optimal allocation to guaranteed contracts is around 50%. The model has different pricing and allocation strategies of selling guaranteed contracts. The maximised revenue is mainly collected: (1) from the expected revenue from selling guaranteed contract for competitive market; (2) from the expected RTB revenue for less-competitive market. Table 2 summarises the overall results of model performance. We compare the model with two RTB settings. The first setting is the expected RTB revenue, given by Sφ (Q − S)/S ; the second setting is the actual RTB
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Figure 2: Example of distributions of winning bids and pay- Figure 3: Example of distributions of winning bids and payment prices of adslot3 (Group 1), where average ξ is 6.64, ment prices of adslot8 (Group 2), where average ξ is 3.62, average payment is 0.93, and average winning bid is 1.00. average payment is 1.20, and average winning bid is 3.30.
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Figure 4: Example of learning the price upper bound for adslot6 (Group 2). φ(ξ) and ϕ(ξ) can be learned from the training data (hourly basis) where LOWESS outperforms polynomial and sigmoid methods with respect to the RMSE metric. Given time t, δ(t) is calculated by an exponential decay function 1.96e−t , then χ(t, ξ(t)) is obtained. π is set to be the maximum value of average bids (hourly basis) in the training set, then a surface of the price upper bound Φ(t) is obtained. revenue reported in dataset (ground truth). Our model shows increased revenues compared to both settings over two groups, validating its revenue maximisation. As discussed in Section 4.2, the revenues of slots in Group 2 have doubled as the less competitive market has greater margin to be optimised – the model increases the payment to value ratio1 from 30.53% to 73.97%. Also, the model adopts different pricing and allocation strategies: steadily increasing guaranteed price and selling more impressions via guaranteed contracts in the competitive market; quickly increasing guaranteed price and selling a small number impressions in advance in the less competitive market.
5
Conclusion
In this paper, we proposed a revenue maximisation model for media sellers in display advertising. It solves the decision-making problem of selling impressions between guaranteed and non-guaranteed channels. The model is based on several assumptions for media buyers’ behaviour, such as risk-aversion, stochastic demand arrivals, and time and price effects. Our experiments show that, by adopt1
In an SP auction, buyers are truth-telling; therefore, their bids reveal their values. The payment to value here is equivalent to the payment to winning bid in Table 1.
ing different pricing and allocation strategies, the proposed model can maximise the seller’s expected total revenue in non-competitive and less competitive markets. In the future, it would be interesting to further investigate the buyers’ strategic behaviour in face of PG and RTB, such as non truth-selling bidding, and discuss how to optimally adapt the pricing and allocation strategies to the strategic buying behaviour.
References [1] M. Anjos, R. Cheng, and C. Currie. Optimal pricing policies for perishable products. European Journal of Operational Research, 166(1):246–254, 2005. [2] S. Balseiro, J. Feldman, V. Mirrokni, and M. Muthukrishnan. Yield optimization of display advertising with ad exchange. In Proceedings of the 12th ACM Conference on Electronic Commerce, pages 27–28, 2011. [3] V. Bharadwaj, P. Chen, W. Ma, C. Nagarajan, J. Tomlin, S. Vassilvitskii, E. Vee, and J. Yang. Shale: an efficient algorithm for allocation of guaranteed display advertising. In Proceedings of the 18th ACM
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Figure 5: Example of optimal allocation and pricing of impressions for adslot3 (Group 1), where the green point in the third plot shows the optimal allcoation γ ∗ = 69%. Arrived demand
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Figure 6: Example of optimal allocation and pricing of impressions for adslot8 (Group 2), where the green point in the third plot shows the optimal allcoation γ ∗ = 54%.
SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2278–2284, 2012. [4] V. Bharadwaj, W. Ma, M. Schwarz, J. Shanmugasundaram, E. Vee, J. Xie, and J. Yang. Pricing guaranteed contracts in online display advertising. In Proceedings of the 19th ACM International Conference on Information and Knowledge Management, pages 399–408, 2010. [5] C. Bishop. Pattern Recognition and Machine Learning. Springer, 2006. [6] B. Chen. Risk-aware dynamic reserve prices of programmatic guarantee in display advertising. In Proceedings of the 16th IEEE International Conference on Data Mining Workshops, pages 511–518, 2016. [7] B. Chen, S. Yuan, and J. Wang. A dynamic pricing model for unifying programmatic guarantee and realtime bidding in display advertising. In Proceedings of the 8th International Workshop on Data Mining for Online Advertising, pages 1–9, 2014.
[8] DoubleClick. The decade in online advertising 19942004. White Paper, 2005. [9] eMarketer. Real-time bidding poised to make up quarter of all display spending. http://goo.gl/ 04Ykx, 2013. [10] J. Feldman, N. Korula, V. Mirrokni, M. Muthukrishnan, and M. P´al. Online ad assignment with free disposal. In Proceedings of the 5th International Workshop on Internet and Network Economics, pages 374– 385, 2009. [11] A. Ghosh, P. McAfee, K. Papineni, and S. Vassilvitskii. Bidding for representative allocations for display advertising. In Proceedings of the 5th International Workshop on Internet and Network Economics, pages 14–18, 2009. [12] J. Kleinberg and E. Tardos. Algorithm Design. Addison Wesley, 2005.
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Revenue increase Model vs expected RTB Model vs ground truth RTB 3.20% (2.65%) 7.10% (2.29%) 95.49% (65.41%) 101.33% (63.03%)
Ratio of selling in advance 81.48% (11.63%) 63.15% (16.15%)
Payment to value 97.19% (1.91%) 73.97% (46.30%)
Table 2: Results of model performance across 26 ad slots. Numbers in round brackets are standard deviations. [13] M. Muthukrishnan. Ad exchanges: research issues. In Proceedings of the 5th International Workshop on Internet and Network Economics, pages 1–12, 2009. [14] Y. Narahari. Game Theory and Mechanism Design. World Scientific, 2014. [15] OpenX. Programmatic + premium: current practices and future trends. White Paper, 2013. [16] M. Ostrovsky and M. Schwarz. Reserve prices in Internet advertising auctions: a field experiment. In Proceedings of the 12th ACM Conference on Electronic Commerce, pages 59–60, 2011. [17] G. Roels and K. Fridgeirsdottir. Dynamic revenue management for online display advertising. Journal of Revenue & Pricing Management, 8(5):452–466, 2009. [18] S. Yuan, J. Wang, B. Chen, P. Mason, and S. Seljan. An empirical study of reserve price optimisation in real-time bidding. In Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1897–1906, 2014. [19] Y. Yuan, F. Wang, J. Li, and R. Qin. A survey on real time bidding advertising. In IEEE International Conference on Service Operations and Logistics, and Informatics, pages 418–423, 2014.
