2000 character limit reached
Pre- and Post-Auction Discounts in First-Price Auctions (2403.06278v1)
Published 10 Mar 2024 in cs.GT
Abstract: One method to offer some bidders a discount in a first-price auction is to augment their bids when selecting a winner but only charge them their original bids should they win. Another method is to use their original bids to select a winner, then charge them a discounted price that is lower than their bid should they win. We show that the two methods have equivalent auction outcomes, for equal additive discounts and for multiplicative ones with appropriate adjustments to discount amounts. As a result, they have corresponding equilibria when equilibria exist. We also show that with the same level of multiplicative adjustments, bidders with discounts should prefer an augmented bid to a discounted price. Then we estimate optimal bid functions for valuation distributions based on data from online advertising auctions, and show how different discount levels affect auction outcomes for those bid functions.
- Mohammad Akbarpour and Shengwu Li. 2020. Credible auctions: A trilemma. Econometrica 88, 2 (2020), 425–467.
- Jason Bigler. 2019. Rolling out first price auctions to Google Ad Manager partners. Consulted at https://www. blog. google/products/admanager/rolling-out-first-price-auctions-google-ad-manager-partners (2019).
- Sam Cox. 2019. Simplifying programmatic: first price auctions for Google Ad Manager. Google Ad Manager (March 6), https://www. blog. google/products/admanager/simplifying-programmaticfirst-price-auctions-google-ad-manager (2019).
- H. A. David and H. N. Nagaraja. 2003. Order Statistics (3 ed.). Wiley.
- First-Price Auctions in Online Display Advertising. Journal of Marketing Research 58, 5 (2021), 888–907. https://doi.org/10.1177/00222437211030201 arXiv:https://doi.org/10.1177/00222437211030201
- Gadi Fibich and Nir Gavish. 2012. Asymmetric First-Price Auctions—A Dynamical-Systems Approach. Mathematics of Operations Research 37, 2 (2012), 219–243. http://www.jstor.org/stable/23256621
- Structural Econometrics of Auctions: A Review. http://dx.doi.org/10.1561/0800000031
- Optimal Nonparametric Estimation of First-Price Auctions. Econometrica 68, 3 (2000), 525–574. http://www.jstor.org/stable/2999600
- Benjamin Heymann and P. Mertikopoulos. 2021. A heuristic for estimating Nash equilibria in first-price auctions with correlated values. ArXiv abs/2108.04506 (2021).
- Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions. Computational Economics 42, 2 (2013), 241–266. https://doi.org/10.1007/s10614-012-9333-z
- Timothy P. Hubbard and Harry J. Paarsch. 2012. On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm. Technical Report.
- René Kirkegaard. 2009. Asymmetric first price auctions. Journal of Economic Theory 144, 4 (2009), 1617–1635. https://doi.org/10.1016/j.jet.2008.12.001
- Elena Krasnokutskaya and Katja Seim. 2011. Bid Preference Programs and Participation in Highway Procurement Auctions. American Economic Review 101, 6 (October 2011), 2653–86. https://doi.org/10.1257/aer.101.6.2653
- Bernard Lebrun. 1999. First Price Auctions in the Asymmetric N Bidder Case. International Economic Review 40, 1 (February 1999), 125–142. https://ideas.repec.org/a/ier/iecrev/v40y1999i1p125-42.html
- Jonathan Levin. 2004. Auction Theory. Stanford University (2004). https://web.stanford.edu/~jdlevin/Econ%20286/Auctions.pdf
- Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator. Journal of Econometrics 211, 2 (aug 2019), 507–538. https://doi.org/10.1016/j.jeconom.2019.02.006
- Justin Marion. 2007. Are Bid Preferences Benign? The Effect of Small Business Subsidies in Highway Procurement Auctions. Journal of Public Economics 91 (08 2007), 1591–1624. https://doi.org/10.1016/j.jpubeco.2006.12.005
- Eric Maskin and John Riley. 2000a. Asymmetric Auctions. The Review of Economic Studies 67 (2000), 413–438. arXiv:https://scholar.harvard.edu/files/maskin/files/asymmetric_auctions.pdf
- Eric Maskin and John Riley. 2000b. Equilibrium in Sealed High Bid Auctions. The Review of Economic Studies 67, 3 (07 2000), 439–454. https://doi.org/10.1111/1467-937X.00138 arXiv:https://academic.oup.com/restud/article-pdf/67/3/439/4422007/67-3-439.pdf
- Eric Maskin and John Riley. 2003. Uniqueness of equilibrium in sealed high-bid auctions. Games and Economic Behavior 45, 2 (2003), 395–409. https://doi.org/10.1016/S0899-8256(03)00150-7 Special Issue in Honor of Robert W. Rosenthal.
- Daniel McFadden. 2003. The Theory of First-Price, Sealed-Bid Auctions. UC Berkeley (2003). https://eml.berkeley.edu/~mcfadden/eC103_f03/auctionlect.pdf
- P. R. Milgrom. 2004. Putting Auction Theory to Work. Cambridge University Press.
- P. R. Milgrom and R. J. Weber. 1982. A Theory of Auctions and Competitive Bidding. Econometrica 50, 5 (1982), 1089–1122.
- R. B. Myerson. 1981. Optimal Auction Design. Mathematics of Operations Research 6, 1 (1981), 58–73.
- Philip Reny and Shmuel Zamir. 2004. On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions. Econometrica 72 (02 2004), 1105–1125. https://doi.org/10.1111/j.1468-0262.2004.00527.x
- J. G. Riley and W. F. Samuelson. 1981. Optimal Auctions. American Economic Review 71, 3 (1981), 381–392.
- W. Vickrey. 1961. Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance 16, 1 (1961), 8–37.
- Bayesian Nash Equilibrium in First-Price Auction with Discrete Value Distributions. In Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems (Auckland, New Zealand) (AAMAS ’20). International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC, 1458–1466.