Expectations-Based Loss Aversion in Auctions with Interdependent Values: Extensive vs. Intensive Risk

We analyze the bidding behavior of expectations-based loss-averse bidders in auctions with interdependent values. We emphasize the difference between the risk bidders face over whether they win the auction (extensive risk) and the risk they face over the value of the prize conditional on winning (intensive risk). The extensive risk creates an “attachment” effect, whereas the intensive risk operates via a “comparison” effect. How loss-averse bidders react to these different risks depends on whether they incorporate their bid into their reference point. Under “unacclimating personal equilibrium” (UPE), where bidders keep their expectations fixed when choosing their bids, both the extensive and intensive risks induce them to bid more aggressively. Moreover, bidders are exposed to the “winner’s curse” and a seller can attain higher revenue by hiding information in order to leverage the intensive risk. By contrast, under “choice-acclimating personal equilibrium” (CPE), where a bid determines both the reference lottery and the outcome lottery, the intensive risk creates a “precautionary bidding” effect that pushes bidders to behave less aggressively; whether this effect is reinforced or undermined by the extensive risk depends on a bidder’s likelihood of winning the auction. Furthermore, bidders are less aggressive than under UPE and can be subject to a “loser’s curse.” Yet, by committing to bidding less aggressively, such as by engaging in proxy bidding, loss-averse bidders are better off under CPE than UPE.