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

Abstract

Please scroll down for article-it is on subsequent pagesWith 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit

Dutch vs. first-price auctions with expectations-based loss-averse bidders

“…In particular, UPE has been extensively used to study firms' pricing and advertising decisions; see, for instance, Heidhues and Kőszegi (2008, 2014) Karle and Peitz (2014, 2017), Karle and Möller (2020), Karle and Schumacher (2017) and Rosato (2016). On the other hand, CPE has been mainly applied to analyze questions in contract theory and mechanism design; see Herweg et al (2010), Lange and Ratan (2010), Eisenhuth (2019), Meisner and von Wanghenheim (2021) and Benkert (2022).4 As shown byBalzer and Rosato (2021), under UPE the FPA and SPA are revenue equivalent; therefore, our results on the reserve price for the FPA carry over to the SPA.…”

“…The first line in (11) represents a type-t bidder's material payoff when mimicking a bidder with type t ≥ t r . The second line represents the expected gain-loss utility from the "extensive risk"the dis-utility stemming from the risk between winning and losing the auction -while the last line depicts the bidder's expected gain-loss utility from the risk in the payment dimension, or the "intensive risk"; see also Balzer and Rosato (2021). Notice that the latter risk is not present in the FPA, where bidders know their payment conditional on winning.…”

“…Both specifications are sensible from a theoretical perspective and have been applied in various economic settings. 3 We refrain from taking a stand on which specification is more appropriate, but point out that the two yield different predictions for bidder behavior.…”

Loss aversion in sequential auctions

“…Furthermore, it is easy to verify that also in the FPA, equilibrium bids are subject to the discouragement effect: the higher is the previous round's winning bid, the less aggressively the remaining bidders will bid in the current round. Finally, as shown by Lange and Ratan (2010) and Balzer and Rosato (2021), the FPA and SPA are revenue equivalent if bidders are not loss averse over money. The reason is that, in this case, the psychological losses depend only on the probability with which a bidder expects to win the auction and, with symmetric strategies, this is the same in both formats.…”

“…in a bidder's overall utility. In the more general case where bidders are loss averse in both dimensions, only those with relatively high types will overbid; see Lange and Ratan (2010), Balzer and Rosato (2021), and von Wangenheim ( 2021). Yet, a similar notion of loss-adjusted willingness to pay also applies if bidders are loss averse in both dimensions.…”