Stochastic Equivalence in Sequential Auctions with New Buyers

Said, Maher (2008): Stochastic Equivalence in Sequential Auctions with New Buyers.

Abstract

We examine markets in which multiple buyers with single-unit demand are faced with an infinite sequence of potential transactions that occur at random times. Moreover, the set and number of buyers are not fixed throughout this sequence; instead, additional buyers may arrive probabilistically on the market in each period. Buyer valuations are independently distributed, and objects are stochastically equivalent. We solve for the expected payoffs of buyers when trade occurs via sequential second-price auctions, and examine the manner in which the option value of future auctions, and hence bidding behavior, varies with both current market conditions and anticipated future dynamics. In addition, we consider the case when buyer valuations are persistent in the sense that distributions are chosen according to a Markov process, and provide a generalization of our result to this setting.

• 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Fuchs, W. and A. Skrzypacz (2008): “Bargaining with Arrival of New Traders,” Unpublished manuscript, Stanford University.

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. (2008): “Information Revelation in Sequential Ascending Auctions,” 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.