Aversion to Price Risk and the Afternoon Effect

Many empirical studies of auctions show that prices of identical goods sold sequentially follow a declining path. Declining prices have been viewed as an anomaly, because the theoretical models of auctions predict that the price sequence should either be a martingale (with independent signals and no informational externalities), or a submartingale (with a¢ liated signals). This paper shows that declining prices, the afternoon e¤ect, arise naturally when bidders are averse to price risk. A bidder is averse to price risk if he prefers to win an object at a certain price, rather than at a random price with the same expected value. When bidders have independent signals and there are no informational externalities, only the e¤ect of aversion to price risk is present and the price sequence is a supermartingale. When there are informational externalities, even with independent signals, there is a countervailing, informational e¤ect, which pushes prices to raise along the path of a sequential auction. This may help explaining the more complex price paths we observe in some auctions. Journal of Economic Literature Classi…cation Numbers: D44, D82. Keywords: Afternoon E¤ect, Declining Price Anomaly, E¢ cient Auctions, Multi-Unit Auctions, Price Risk, Revenue Equivalence, Risk Aversion, Sequential Auctions. I have bene…ted from many useful comments during presentations of preliminary, unwritten, versions of this paper. I would like to thank the audiences at the 2007 Advancement of Economic Theory Conference in Kos, the Competition Authority of Portugal, and the Universities of Birmingham, Bocconi, Bristol, Core, Essex, LSE, Insead, Institut d’Analisi Economica Barcelona, Napoli/Salerno, Nottingham, Padova, Pompeu Fabra, Reading, Southampton, UCL, Warwick.