Sequential auctions, price trends, and risk preferences

We analyze sequential auctions in a general environment where bidders are heterogeneous in risk exposures and exhibit non-quasilinear utilities. We derive a pure strategy symmetric equilibrium for the sequential Dutch and Vickrey auctions respectively, with an arbitrary number of identical objects for sale. When bidders are risk averse (preferring), the equilibrium price sequences must be downward (upward) drifting. The "declining price anomaly" is thus evidence of bidder risk aversion in this general environment. These results derive from a key assumption that bidders' marginal utilities are log-supermodular in payment and type.