# Reserve prices in repeated auctions

- 167 Downloads

## Abstract

I consider a model of repeated auctions in which the distribution of bidders’ values is only known to the bidders and the seller attempts to learn this distribution to inform her choice of reserve prices in the future. I find that in any equilibrium bidders will shade their bids to act as if their values are drawn from a lower distribution than they actually are. The bid shading may be so severe that the seller would prefer to simply commit to setting the reserve price that would be optimal if bidders’ values were drawn from the lowest possible distribution to eliminate the incentive for bidders to shade their bids.

## Keywords

Repeated auctions Reserve prices Bid shading## JEL Classification

C72 D44 D80 D82## Notes

### Acknowledgements

I thank Chris Harris, Preston McAfee, Sergei Vassilvitskii, the anonymous associate editor, and the anonymous referees for helpful comments and discussions.

## References

- Acquisiti A, Varian HR (2005) Conditioning prices on purchase history. Mark Sci 24(3):367–381CrossRefGoogle Scholar
- Amin K, Rostamizadeh A, Syed U (2013) Learning prices for repeated auctions with strategic buyers. Adv Neural Inf Process Syst 26:1169–1177Google Scholar
- Aoyagi M (2003) Bid rotation and collusion in repeated auctions. J Econ Theory 112(1):79–105CrossRefGoogle Scholar
- Bernhardt D, Scoones D (1994) A note on sequential auctions. Am Econ Rev 84(3):653–657Google Scholar
- Besanko D, Winston WL (1990) Optimal price skimming by a monopolist facing rational consumers. Manag Sci 36(5):555–567CrossRefGoogle Scholar
- Caillaud B, Mezzetti C (2004) Equilibrium reserve prices in sequential ascending auctions. J Econ Theory 117(1):78–95CrossRefGoogle Scholar
- Cho M, Fan M, Zhou YP (2009) Strategic consumer response to dynamic pricing of perishable products. In: Netessine S, Tang CS (eds) Consumer-driven demand and operations management models: a systematic study of information-technology-enabled sales mechanisms. Springer, Dordrecht, pp 435–457CrossRefGoogle Scholar
- Coase RH (1972) Durability and monopoly. J Law Econ 15(1):143–149CrossRefGoogle Scholar
- Devanur NR, Peres Y, Sivan B (2015) Perfect Bayesian equilibria in repeated sales. Proc Symp Discret Algorithms 26:983–1002Google Scholar
- Freixas X, Guesnerie R, Tirole J (1985) Planning under incomplete information and the ratchet effect. Rev Econ Stud 52(2):173–191CrossRefGoogle Scholar
- Fudenberg D, Villas-Boas JM (2007) Behavior-based price discrimination and customer recognition. In: Hendershott T (ed) Economics and information systems, vol 1. Emerald Group Publishing Limited, Bingley, pp 377–436CrossRefGoogle Scholar
- Gul F, Sonnenschein H, Wilson R (1986) Foundations of dynamic monopoly and the Coase conjecture. J Econ Theory 39(1):155–190CrossRefGoogle Scholar
- Hart OD, Tirole J (1988) Contract renegotiation and Coasian dynamics. Rev Econ Stud 55(4):509–540CrossRefGoogle Scholar
- Jeitschko TD (1999) Equilibrium price paths in sequential auctions with stochastic supply. Econ Lett 64(1):67–72CrossRefGoogle Scholar
- Krishna V (2010) Auction theory. Academic Press, BurlingtonGoogle Scholar
- LaCasse C (1995) Bid rigging and the threat of government prosecution. RAND J Econ 26(3):398–417CrossRefGoogle Scholar
- Laffont JJ, Tirole J (1988) The dynamics of incentive contracts. Econometrica 56(5):1153–1175CrossRefGoogle Scholar
- Lahaie S, McAfee RP (2011) Efficient ranking in sponsored search. Proc Int Worksh Internet Netw Econ (WINE) 7:254–265CrossRefGoogle Scholar
- Lavi R, Segev E (2014) Efficient levels in sequential auctions with dynamic arrivals. Int J Game Theory 43(4):791–819CrossRefGoogle Scholar
- Liu Q, Mierendorff K, Shi X, Zhong W (2017) Auctions with limited commitment. Columbia University, TypescriptGoogle Scholar
- Luton R, McAfee RP (1986) Sequential procurement auctions. J Public Econ 31(2):181–195CrossRefGoogle Scholar
- McAfee RP, Vincent D (1993) The declining price anomaly. J Econ Theory 60(1):191–212CrossRefGoogle Scholar
- McAfee RP, Vincent D (1997) Sequentially optimal auctions. Games Econ Behav 18(2):246–276CrossRefGoogle Scholar
- Menezes FM, Ryan MJ (2009) Coasian dynamics in repeated English auctions. Int J Game Theory 38(3):349–366CrossRefGoogle Scholar
- Milgrom P, Weber R (2000) A theory of auctions and competitive bidding, ii. In: Klemperer P (ed) The economic theory of auctions. Edward Elgar Publishing, Cheltnam, pp 179–194Google Scholar
- Myerson RB (1981) Optimal auction design. Math Oper Res 6(1):58–73CrossRefGoogle Scholar
- Ostrovsky M, Schwarz M (2016) Reserve prices in Internet advertising auctions: a field experiment. Typescript. Stanford Graduate School of Business, StanfordGoogle Scholar
- Pai M, Vohra R (2013) Optimal dynamic auctions and simple index rules. Math Oper Res 38(4):682–697CrossRefGoogle Scholar
- Parberry I (1994) Problems on algorithms, 1st edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
- Schmidt KM (1993) Commitment through incomplete information in a simple repeated bargaining game. J Econ Theory 60(1):114–139CrossRefGoogle Scholar
- Skreta V (2006) Sequentially optimal mechanisms. Rev Econ Stud 73(4):1085–1111CrossRefGoogle Scholar
- Skreta V (2015) Optimal auction design under non-commitment. J Econ Theory 159(B):854–890CrossRefGoogle Scholar
- Sun Y, Zhou Y, Deng X (2014) Optimal reserve prices in weighted GSP auctions. Electron Commer Res Appl 13(3):178–187CrossRefGoogle Scholar
- Vulcano G, van Ryzin G, Maglaras C (2002) Optimal dynamic auctions for revenue management. Manag Sci 48(11):1388–1407CrossRefGoogle Scholar
- Zeithammer R (2007) Strategic bid-shading and sequential auctioning with learning from past prices. Manag Sci 53(9):1510–1517CrossRefGoogle Scholar
- Zheng CZ (2002) Optimal auction with resale. Econometrica 70(6):2197–2224CrossRefGoogle Scholar