Sealed Bid Second Price Auctions with Discrete Bidding

Applied Economics Research Bulletin, Vol. 1, No. 1, pp. 31-52, 2008

22 Pages Posted: 13 Feb 2009 Last revised: 25 Mar 2009

See all articles by Timothy Mathews

Timothy Mathews

Kennesaw State University - Michael J. Coles College of Business

Abhijit Sengupta

Surrey Business School, University of Surrey

Abstract

A single item is sold to two bidders by way of a sealed bid second price auction in which bids are restricted to a set of discrete values. Restricting attention to symmetric pure strategy behavior on the part of bidders, a unique equilibrium exists. When following these equilibrium strategies bidders may bid strictly above or below their valuation, implying that the item may be awarded to a bidder other than the high valuation bidder. In an auction with two acceptable bids, the expected revenue of the seller may be maximized by a high bid level not equal to the highest possible bidder valuation and may exceed the expected revenue from an analogous second price auction with continuous bidding (and no reserve price). With three acceptable bids, a revenue maximizing seller may choose unevenly spaced bids. With an arbitrary number of evenly spaced bids, as the number of acceptable bids is increased, the expected revenue of the seller and the probability of ex post inefficiency both may either increase or decrease.

Keywords: Auctions/Bidding, Auction Design, Discrete Bidding

JEL Classification: D11, D44

Suggested Citation

Mathews, Timothy and Sengupta, Abhijit, Sealed Bid Second Price Auctions with Discrete Bidding. Applied Economics Research Bulletin, Vol. 1, No. 1, pp. 31-52, 2008, Available at SSRN: https://ssrn.com/abstract=1341709

Timothy Mathews (Contact Author)

Kennesaw State University - Michael J. Coles College of Business ( email )

1000 Chastain Road
Kennesaw, GA 30144
United States

Abhijit Sengupta

Surrey Business School, University of Surrey ( email )

Guildford, Surrey GU2 7XH
United Kingdom

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