Sequential Auctions with Randomly Arriving Buyers

Said, Maher (2009): Sequential Auctions with Randomly Arriving Buyers.

Abstract

We analyze a dynamic market in which buyers compete in a sequence of auctions. New buyers and objects may arrive at random times. Buyers' private values, however, are not persistent. Instead, buyers draw new values in every period; equivalently, objects are heterogeneous but are drawn from the same distribution.

We consider the use of the second-price auction for selling these objects. In equilibrium, buyers do not bid their true value. Instead, they shade their bids down by their continuation value, which is the option value of participating in future auctions. We show that this option value depends not only on the number of buyers currently present on the market, but also on anticipated market dynamics. We also generalize our results to the setting in which values correspond to a "buyer's market" or a "seller's market" and market conditions evolve, with persistence, from one to the other.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic markets, Random arrivals, Endogenous option value, Sequential auctions, Stochastic equivalence.
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Arnold, B. C. and R. A. Groeneveld (1979): “Bounds on Expectations of Linear Systematic Statistics Based on Dependent Samples,” Annals of Statistics, 7, 220–223.

Bartoszewicz, J. (1986): “Dispersive Ordering and the Total Time on Test Transformation,” Statistics and Probability Letters, 4, 285–288.

Boland, P.J., M. Shaked, and J.G. Shanthikumar (1998): “Stochastic Ordering of Order Statistics,” in Handbook of Statistics, ed. by N. Balakrishnan and C. Rao, Elsevier, vol. 16, chap. 5, 89–103.

David, H. and H. Nagaraja (2003): Order Statistics, Wiley-Interscience, 3 ed.

Elayedi, S. (2005): An Introduction to Difference Equations, Springer, 3 ed.

Engelbrecht-Wiggans, R. (1994): “Sequential Auctions of Stochastically Equivalent Objects,” Economics Letters, 44, 87–90.

Fuchs, W. and A. Skrzypacz (2008): “Bargaining with Arrival of New Traders,” American Economic Review, forthcoming.

Inderst, R. (2008): “Dynamic Bilateral Bargaining under Private Information with a Sequence of Potential Buyers,” Review of Economic Dynamics, 11, 220–236.

Kochar, S. (1999): “On Stochastic Orderings Between Distributions and their Sample Spacings,” Statistics and Probability Letters, 42, 345–352.

Krishna, V. (2002): Auction Theory, San Diego: Academic Press.

Nekipelov, D. (2007): “Entry Deterrence and Learning Prevention on eBay,” Unpublished manuscript, Duke University.

Said, M. (2009): “Auctions with Dynamic Populations: Efficiency and Revenue Maximization,” Unpublished manuscript, Yale University.

Sailer, K. (2006): “Searching the eBay Marketplace,” CESifo Working Paper 1848, University of Munich.

Satterthwaite, M. and A. Shneyerov (2007): “Dynamic Matching, Two-Sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition,” Econometrica, 75, 155–200.

Taylor, C. (1995): “The Long Side of the Market and the Short End of the Stick: Bargaining Power and Price Formation in Buyers’, Sellers’, and Balanced Markets,” Quarterly Journal of Economics, 110, 837–855.

Xu, M. and X. Li (2006): “Likelihood Ratio Order of m-spacings for Two Samples,” Journal of Statistical Planning and Inference, 136, 4250–4258.

Zeithammer, R. (2006): “Forward-Looking Bidding in Online Auctions,” Journal of Marketing Research, 43, 462–476.