Auctions with Limited Commitment
We study auction design in the standard symmetric independent private values environment, where the seller lacks the commitment power to withhold an unsold object off the market. The seller has a single object and can conduct an infinite sequence of standard auctions with reserve prices to maximize her expected profit. In each period, the seller can commit to a reserve price for the current period but cannot commit to future reserve prices. We analyze the problem with limited commitment through an auxiliary mechanism design problem with full commitment, in which an additional constraint reflects the sequential rationality of the seller. We characterize the maximal profit achievable in any perfect Bayesian equilibrium in the limit as the period length vanishes. The static full commitment profit is not achievable but the seller can always guarantee the profit of an efficient auction. If the number of buyers exceeds a cutoff which is small for many distributions, the efficient auction is optimal. Otherwise, the efficient auction is not optimal, and we give conditions under which the optimal solution consists of an initial auction with a non-trivial reserve price followed by a continuously decreasing price path. The solution is described by a simple ordinary differential equation. Our analysis combines insights from bargaining, auctions, and mechanism design.
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- Bester, Helmut & Strausz, Roland, 2000. "Imperfect commitment and the revelation principle: the multi-agent case," Economics Letters, Elsevier, vol. 69(2), pages 165-171, November.
- Johannes Hörner & Larry Samuelson, 2011.
"Managing Strategic Buyers,"
Journal of Political Economy,
University of Chicago Press, vol. 119(3), pages 379-425.
- Johannes Horner & Larry Samuelson, 2008. "Managing Strategic Buyers," Cowles Foundation Discussion Papers 1684R, Cowles Foundation for Research in Economics, Yale University, revised Sep 2010.
- Johannes Horner & Larry Samuelson, 2009. "Managing Strategic Buyers," Levine's Working Paper Archive 814577000000000059, David K. Levine.
- Johannes Horner & Larry Samuelson, 2010. "Managing Strategic Buyers," Levine's Working Paper Archive 661465000000000279, David K. Levine.
- Johannes Horner & Larry Samuelson, 2011. "Managing Strategic Buyers," Levine's Working Paper Archive 786969000000000025, David K. Levine.
- Hannu Vartiainen, 2013. "Auction Design Without Commitment," Journal of the European Economic Association, European Economic Association, vol. 11(2), pages 316-342, April.
- Hannu Vartiainen, 2003. "Auction Design without Commitment," Working Papers 2003.24, Fondazione Eni Enrico Mattei.
- Hannu Vartiainen, 2009. "Auction Design without Commitment," Discussion Papers 44, Aboa Centre for Economics.
- David McAdams & Michael Schwarz, 2007. "Credible Sales Mechanisms and Intermediaries," American Economic Review, American Economic Association, vol. 97(1), pages 260-276, March.
- William Fuchs & Andrzej Skrzypacz, 2010. "Bargaining with Arrival of New Traders," American Economic Review, American Economic Association, vol. 100(3), pages 802-836, June.
- Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
- Krishna, Vijay, 2002. "Auction Theory," Elsevier Monographs, Elsevier, edition 1, number 9780124262973.
- Sobel, Joel, 1991. "Durable Goods Monopoly with Entry of New Consumers," Econometrica, Econometric Society, vol. 59(5), pages 1455-1485, September.
- Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
- Bulow, Jeremy I, 1982. "Durable-Goods Monopolists," Journal of Political Economy, University of Chicago Press, vol. 90(2), pages 314-332, April.
- Mathias Dewatripont, 1989. "Renegotiation and Information Revelation Over Time: The Case of Optimal Labor Contracts," The Quarterly Journal of Economics, Oxford University Press, vol. 104(3), pages 589-619.
- Simon Board & Andrzej Skrzypacz, 2016. "Revenue Management with Forward-Looking Buyers," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1046-1087.
- Andrzej Skrzypacz & Simon Board, 2011. "Revenue Management with Forward-Looking Buyers," 2011 Meeting Papers 87, Society for Economic Dynamics.
- Nancy L. Stokey, 1981. "Rational Expectations and Durable Goods Pricing," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 112-128, Spring.
- Wolitzky, Alexander, 2010. "Dynamic monopoly with relational incentives," Theoretical Economics, Econometric Society, vol. 5(3), September.
- Chia-Hui Chen, 2012. "Name Your Own Price at Priceline.com: Strategic Bidding and Lockout Periods," Review of Economic Studies, Oxford University Press, vol. 79(4), pages 1341-1369.
- Oliver D. Hart & Jean Tirole, 1988. "Contract Renegotiation and Coasian Dynamics," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 509-540.
- Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
- Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
- Gershkov, Alex & Moldovanu, Benny, 2012. "Dynamic allocation and pricing: A mechanism design approach," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 283-286. Full references (including those not matched with items on IDEAS)
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