On the Role of Ad Networks: To Endogenize or Not to Endogenize the Number of Bidders in Auctions?

Parneet Pahwa

doi:10.1515/roms-2022-0032

Article

On the Role of Ad Networks: To Endogenize or Not to Endogenize the Number of Bidders in Auctions?

Parneet Pahwa

Published/Copyright: October 5, 2022

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Review of Marketing Science Volume 20 Issue 1

Abstract

In the world of online advertising, demand for banner slots by advertisers is matched with the inventory available at different publishers by an intermediary (Ad Network or an Exchange). One important feature of auctions in the online advertising space is that publishers typically have multiple slots and advertisers are not necessarily interested in purchasing one unit but are rather interested in purchasing thousands of impressions. Furthermore, an ad network may have different types of publishers with varying quality of advertising space available. Consequently, bidders may value slots in one set of publishers very differently from slots in a different set. For instance, firms selling financial products and services may value slots at CNN.com’s financial section or WSJ.com very differently from slots available at people.com or even the weather section in CNN.com. So, the dilemma confronting an ad network that has inventory from different publishers, facing demand from say, advertisers selling financial products is whether to pool the inventory and conduct a single auction or conduct separate auctions so that the advertisers know that they are bidding for slots on CNN.com’s financial section or on WSJ.com and not for slots on the weather section on CNN.com or some other less preferred slots. Given the critical role that ad networks play, in serving the request of advertisers to get their advertising banners displayed in online media we examine the economic incentives of these intermediaries to derive implications for the optimal market design. More specifically, we seek answers to the following questions. Given the variation in the quality of inventory available from different publishers under what market conditions should the intermediary pool the inventory across the different publishers and conduct a single (undisclosed) auction and when would it be more profitable to conduct different (disclosed) auctions? Given a fixed number of bidders, if the intermediary chooses to conduct two auctions how many bidders should be allocated to each auction and how do market parameters such as the number of bidders or the inventory available of each type affect the allocation rule. Finally, if the intermediary chooses to conduct two auctions should they charge the same commission or different commissions in each auction? We find that when the number of advertisers is small then pooling inventory and conducting a single auction is the optimal strategy. Under these conditions when the inventory of the publishers is sufficiently differentiated it may even be optimal for the intermediary to conduct a single auction but ignore the inventory of the publisher that is valued lower. When the number of advertisers is large, we find very interestingly that conducting multiple auctions is not always optimal. Indeed, when the inventory of publishers is sufficiently differentiated conducting a single auction and ignoring the inventory of the publisher that is valued lower can still be optimal. We also identify market conditions when conducting two auctions and charging a single commission in both markets is more profitable than conducting two auctions and charging separate commissions (and vice versa).

Keywords: Ad Networks; second-price auctions; endogenizing number of bidders in auctions; game-theory

Corresponding author: Parneet Pahwa, Naveen Jindal School of Management, The University of Texas at Dallas, 800 W Campbell Rd., Richardson, TX 75080, USA, E-mail: parneet.pahwa@utdallas.edu

Appendix

Properties of the Expected Price in a Uniform Price Auction

Let Q denote the inventory available and x denote the number of slots demanded by each advertiser. Assume that each advertiser i’s valuation, V _i is independent and identically distributed and follows a uniform distribution: V _i ∼ U[0, 1]. Given the available inventory and the demand it is easy to see that the intermediary can satisfy the demand of k advertisers where k = Q x . With the uniform price auction the winning bidders will then pay the highest loosing bid, which will be the k + 1 bid. When the valuations are uniformly distributed it is well known that the expected value of the k + 1 order statistic is:

E [ V ( k + 1 ) ] = n − ( k + 1 ) n + 1

Substituting k = Q x in the above equation we obtain:

E [ V ( k + 1 ) ] = n − ( Q x + 1 ) n + 1

Note that:

∂ E [ V ( k + 1 ) ] ∂ n = ( Q x + 2 ) ( n + 1 ) 2 > 0 , ∂ 2 E [ V ( k + 1 ) ] ∂ n 2 = − 2 ( Q x + 2 ) ( n + 1 ) 3 < 0 , ∂ E [ V ( k + 1 ) ] ∂ Q = − 1 x < 0

The expected price is increasing but concave in the number of bidders and decreasing in the inventory available.

References

Bajari, P., and A. Hortacsu. 2000. Winner’s Curse, Reverse Prices, and Endogenous Entry: Empirical Insights from eBay Auctions, Working Paper. Stanford: Stanford University.10.2139/ssrn.224950Search in Google Scholar

Ballesteros-Perez, P., M. C. Gonzalez-Cruz, J. L. Fuentes-Bargues, and M. Skitmore. 2015. “Analysis of the Distribution of the Number of Bidders in Construction Contract Auctions.” Construction Management and Economics 33 (9): 752–70.10.1080/01446193.2015.1090008Search in Google Scholar

Bapna, R., P. Goes, and A. Gupta. 2001. “On-Line Auctions: Insights and Analysis.” Communications of the ACM 44 (110): 42–50.10.1145/384150.384160Search in Google Scholar

Board, S. 2009. “Revealing Information in Auctions: The Allocation Effect.” Economic Theory 38 (1): 125–35, https://doi.org/10.1007/s00199-006-0177-4.Search in Google Scholar

Cassady, R. 1967. Auctions and Auctioneering. Berkeley: University of California Press.10.1525/9780520322257Search in Google Scholar

Easley, R., and R. Tenorio. 1999. Jump Bidding Strategies in Internet Auctions, Working Paper. Notre Dame: Notre Dame University.10.2139/ssrn.170028Search in Google Scholar

Engelbrecht-Wiggans, R. 1993. “Optimal Auctions Revisited.” Games and Economic Behavior 5 (2): 227–39, https://doi.org/10.1006/game.1993.1013.Search in Google Scholar

Evans, D. S. 2008. “The Economics of the Online Advertising Industry.” Review of Network Economics 7 (3): 359–91, https://doi.org/10.2202/1446-9022.1154.Search in Google Scholar

Evans, D. S. 2009. “The Online Advertising Industry: Economics, Evolution, and Privacy, Forthcoming.” Journal of Economic Perspectives 23 (3): 37–60.10.1257/jep.23.3.37Search in Google Scholar

Issac, M., S. Pevnitskaya, and K. S. Schnier. 2012. “Individual Behavior and Bidding Heterogeneity in Sealed Bid Auctions Where the Number of Bidders is Unkown.” Economic Inquiry 50 (2): 516–33.10.1111/j.1465-7295.2011.00393.xSearch in Google Scholar

Kaiser, L., and M. Kaiser. 1999. The Official eBay Guide. New York: Fireside.Search in Google Scholar

Kitts, B., and B. Leblanc. 2004. “Optimal Bidding on Keyword Auctions.” Electronic Markets 14 (3): 186–201, https://doi.org/10.1080/1019678042000245119.Search in Google Scholar

Klein, S., and R. O’Keefe. 1999. “The Impact of Web on Auctions: Some Empirical Evidence and Theoretical Considerations.” International Journal of Electronic Commerce 3 (3): 7–20, https://doi.org/10.1080/10864415.1999.11518338.Search in Google Scholar

Klein, S. 1997. “Introduction to Electronic Auctions.” Electronic Markets 7 (4): 3–6, https://doi.org/10.1080/10196789700000041.Search in Google Scholar

Klemperer, P. 1999. “Auction Theory: A Guide to the Literature.” Journal of Economic Surveys 13 (3): 227–86, https://doi.org/10.1111/1467-6419.00083.Search in Google Scholar

Klemperer, P. 2000. The Economic Theory of Auctions. Cheltenham: Edward Elgar.Search in Google Scholar

Levin, D., and E. Ozdernoren. 2004. “Auctions with Uncertain Number of Bidders.” Journal of Economic Theory 118 (2): 229–51, https://doi.org/10.1016/j.jet.2003.11.007.Search in Google Scholar

Liu, D., and J. Chen. 2006. “Designing Online Auctions with Past Performance Information.” Decision Support Systems 42: 1307–20, https://doi.org/10.1016/j.dss.2005.10.012.Search in Google Scholar

Lucking-Reiley, D. 1999. “Using Field Experiments to Test Equivalence Between Auction Formats: Magic on the Internet.” The American Economic Review 89 (5): 1063–80, https://doi.org/10.1257/aer.89.5.1063.Search in Google Scholar

Lucking-Reiley, D. 2000. “Auctions on the Internet: What’s Being Auctioned, and How?” The Journal of Industrial Economics 48 (3): 227–52, https://doi.org/10.1111/1467-6451.00122.Search in Google Scholar

McAfee, R. P., and J. McMillan. 1987a. “Auctions and Bidding.” Journal of Economic Literature 25: 699–738.Search in Google Scholar

McAfee, R. P., and J. McMillan. 1987b. “Auctions with Stochastic Number of Bidders.” Journal of Economics Theory 43 (1): 1–19, https://doi.org/10.1016/0022-0531(87)90113-x.Search in Google Scholar

Milgrom, P. 1989. “Auctions and Bidding: A Primer.” The Journal of Economic Perspectives 3: 3–22, https://doi.org/10.1257/jep.3.3.3.Search in Google Scholar

Milgrom, P. 2000. An Economist’s Vision of the B-To-B Marketplace. Executive White Paper. Also available at www.perfect.com.Search in Google Scholar

Milgrom, P., and R. Weber. 1982. “A Theory of Auctions and Competitive Bidding.” Econometrica 50 (5): 1089–122, https://doi.org/10.2307/1911865.Search in Google Scholar

Muthukrishnan, S. 2009. “Ad Exchanges: Research Issues.” WINE 2009, LNCS 5929: 1–12, https://doi.org/10.1145/1980522.1980531.Search in Google Scholar

Peckec, A. S., and I. Tsetlin. 2008. “Revenue Ranking of Discriminatory and Uniform Auctions with an Number of Bidders.” Management Science 54 (9): 1610–23.10.1287/mnsc.1080.0882Search in Google Scholar

Pinker, E. J., A. Siedmann, and Y. Vakrat. 2003. “Managing Online Auctions: Current Business and Research Issues.” Management Science v49 (n11): 1457–84, https://doi.org/10.1287/mnsc.49.11.1457.20584.Search in Google Scholar

Rothkopf, M., and R. Harstad. 1994. “Modeling Competitive Bidding: A Critical Essay.” Management Science 40 (3): 364–84, https://doi.org/10.1287/mnsc.40.3.364.Search in Google Scholar

Stark, R. M., and M. Rothkopf. 1979. “Competitive Bidding: A Comprehensive Bibliography.” Operations Research 27: 364–90, https://doi.org/10.1287/opre.27.2.364.Search in Google Scholar

Vakrat, Y. 2000. “Optimal Design of Online Auctions.” Unpublised PhD thesis. University of Rochester. Rochester.Search in Google Scholar

Van Heck, E., and P. Vervest. 1998. “How Should CIOs Deal with Web Based Auctions?” Communications of the ACM 41 (7): 99–100, https://doi.org/10.1145/278476.278495.Search in Google Scholar

Wurmann, P., M. P. Wellman, and W. E. Walsh. 2001. “A Parameterization of the Auction Design Space.” Games and Economic Behavior 38: 304–38, https://doi.org/10.1006/game.2000.0828.Search in Google Scholar

Received: 2022-04-11

Accepted: 2022-09-10

Published Online: 2022-10-05

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/roms-2022-0032

Keywords for this article

Ad Networks; second-price auctions; endogenizing number of bidders in auctions; game-theory