Sequential auctions, price trends, and risk preferences

We analyze sequential auctions where bidders are heterogeneous in risk exposures and exhibit non-quasilinear utilities. We derive an increasing pure strategy equilibrium for the sequential Dutch and Vickrey auctions respectively, with an arbitrary number of identical objects for sale. A suffi cient, and to certain extent necessary, condition for this result is that bidders’marginal utilities are log-submodular in income and type. This condition is fairly general, and in the environment we consider implies that both the Dutch and Vickrey sequential auctions are ex post effi cient. We then show that when bidders are risk averse (preferring), the equilibrium price sequences must be downward (upward) drifting. In particular, the “declining price anomaly” is perfectly consistent with nonincreasing absolute risk aversion when bidders have exposures to background risks– that is, when failure of acquiring the auctioned object entails negative consequences.