# An equilibrium analysis of a core-selecting package auction with reserve prices

Original Paper

First Online:

Received:

Accepted:

- 39 Downloads

## Abstract

This study analyzes the equilibrium of a core-selecting package auction under incomplete information. The ascending proxy auction of Ausubel and Milgrom (Front Theor Econ 1:1–42, 2002) is considered in a stylized environment with two goods, two local bidders, and one global bidder. Local bidders shade bids in the equilibrium because of the free-riding incentive. We examine the effect of reserve prices. We show that a reserve price for individual goods increases the equilibrium local bids, whereas they may be decreased by a reserve price for the package of goods. A flexible non-monotonic reserve price rule can improve allocative efficiency as well as seller revenue in the equilibrium.

## Keywords

Core-selecting auction Package auction Ascending proxy auction Reserve price## JEL Classification

D44 D47## References

- Ausubel LM, Baranov O (2010) Core-selecting auctions with incomplete information. Working paper, University of MarylandGoogle Scholar
- Ausubel LM, Baranov O (2014) Market design and the evolution of the combinatorial clock auction. Am Econ Rev 104:446–451CrossRefGoogle Scholar
- Ausubel LM, Baranov O (2017) A practical guide to the combinatorial clock auction. Econ J 127:F334–F350CrossRefGoogle Scholar
- Ausubel LM, Cramton P (2004) Vickrey auction with reserve pricing. Econ Theory 23:493–505CrossRefGoogle Scholar
- Ausubel LM, Milgrom P (2002) Ascending auctions with package bidding. Front Theor Econ 1:1–42CrossRefGoogle Scholar
- Ausubel LM, Milgrom P (2006a) The lovely but lonely vickrey auction. In: Cramton P, Shoham Y, Steinberg R (eds) Combinatorial auctions. MIT Press, Cambridge, pp 17–40Google Scholar
- Ausubel LM, Milgrom P (2006b) Ascending proxy auctions. In: Cramton P, Shoham Y, Steinberg R (eds) Combinatorial auctions. MIT Press, Cambridge, pp 79–98Google Scholar
- Beck M, Ott M (2013) Nash equilibria of sealed-bid package auctions. Working paper, RWTH Aachen UniversityGoogle Scholar
- Clarke EH (1971) Multipart pricing of public goods. Public Choice 11:17–33CrossRefGoogle Scholar
- Cramton P (2013) Spectrum auction design. Rev Ind Organ 42:161–190CrossRefGoogle Scholar
- Day R, Cramton P (2012) Quadratic core-selecting payment rules for combinatorial auctions. Oper Res 60:588–603CrossRefGoogle Scholar
- Day R, Milgrom P (2008) Core-selecting package auctions. Int J Game Theory 36:393–407CrossRefGoogle Scholar
- Erdil A, Klemperer P (2010) A new payment rule for core-selecting package auctions. J Eur Econ Assoc 8:537–547CrossRefGoogle Scholar
- Goeree JK, Lien Y (2016) On the impossibility of core-selecting package auctions. Theor Econ 11:41–52CrossRefGoogle Scholar
- Groves T (1973) Incentives in teams. Econometrica 41:617–631CrossRefGoogle Scholar
- Guth W, Hellwig M (1986) The private supply of a public good. J Econ Suppl 5:121–159CrossRefGoogle Scholar
- Hafalir IE, Yektas H (2015) Core deviation minimizing auctions. Int J Game Thery 44:367–376CrossRefGoogle Scholar
- Hatfield J, Milgrom P (2005) Matching with contracts. Am Econ Rev 95:913–935CrossRefGoogle Scholar
- Kelso A, Crawford VP (1982) Job matching, coalition formation, and gross substitutes. Econometrica 50:1483–1504CrossRefGoogle Scholar
- Lamy L (2012) On minimal ascending auctions with payment discounts. Games Econ Behav 75:990–999CrossRefGoogle Scholar
- Ledyard J (2007) Optimal combinatoric auctions with single-minded bidders. In: Proceedings of the 8th ACM conference on electronic commerce, pp 237–242Google Scholar
- Myerson R (1981) Optimal auction design. Math Oper Res 6:58–73CrossRefGoogle Scholar
- Myerson R, Satterthwaite A (1983) Efficient mechanisms for bilateral trading. J Econ Theory 29:265–281CrossRefGoogle Scholar
- Parkes DC, Ungar LH (2000) Iterative combinatorial auctions: theory and practice. In: Proceedings of the 17th national conference on artificial intelligence (AAAI-2000), pp 74–81Google Scholar
- Sano R (2010) An equilibrium analysis of a package auction with single-minded bidders. Working paper, available at SSRN: http://ssrn.com/abstract=1594471. Accessed 20 June 2018.
- Sano R (2011) Incentives in core-selecting auctions with single-minded bidders. Games Econ Behav 72:602–606CrossRefGoogle Scholar
- Sano R (2012) Non-bidding equilibrium of an ascending core-selecting auction. Games Econ Behav 74:637–650CrossRefGoogle Scholar
- Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Finance 16:8–37CrossRefGoogle Scholar

## Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018