Sequential Auctions, Price Trends, and Risk Preferences
Tinbergen Institute Discussion Paper 14-139/I
34 Pages Posted: 21 Oct 2014
Date Written: October 15, 2014
Abstract
We analyze sequential Dutch and Vickrey auctions where risk averse, or risk preferring, bidders may have heterogeneous risk exposures. We derive and characterize a pure strategy equilibrium of both auctions for arbitrary number of identical objects. A sufficient, and to certain extent necessary, condition for this result is that bidders' marginal utilities are log-submodular in income and type. We then show that when bidders are risk averse (preferring), the equilibrium price sequences should be downward (upward) drifting, and in each period the conditional expected revenue is higher (lower) in the Dutch than in the Vickrey sequential auctions. In particular, the "declining price anomaly" is perfectly consistent with nonincreasing absolute risk aversion when bidders have exposures to background risk.
Keywords: sequential auction, background risk, risk preferences, declining prices, log-submodularity
JEL Classification: D44, D82
Suggested Citation: Suggested Citation