Reference-Dependent Bidding in Dynamic Auctions

Abstract

We investigate equilibrium bidding behavior of bidders with reference-dependent preferences and independent private values in single-unit English and Dutch clock auctions. Bidders' reference points are endogenous and determined by their strategy and their beliefs about the other bidders. In deriving their strategy, bidders anticipate changes in their reference point due to updated information about others' values (i.e., the own winning probability) during the course of the auction, and make optimal binary decisions at each price (approve or quit in the English auction and wait or bid in the Dutch auction). First, we solve for personal equilibrium profiles, i.e., profiles of bids that contain for each bidder a bidding strategy that is optimal given the others' bidding strategies and the reference point induced by the own and others' strategies. Second, we consider locally preferred personal equilibrium (LPPE) profiles, i.e., personal equilibrium profiles where no bidder can locally find a better personal equilibrium given the others' fixed strategies by varying his reference point via considering different own strategies. The expected revenue in the Dutch auction is higher than in the English auction in the respective unique LPPE profiles. The difference is mainly driven by the aversion to losing the item in the Dutch auction.