Auctions with loss‐averse bidders

• Author: Mara Grunewald,Roland Eisenhuth
• Published date: 01 June 2020
• Date: 01 June 2020
• DOI: http://doi.org/10.1111/ijet.12189

doi: 10.1111/ijet.12189

Auctions with loss-averse bidders

Roland Eisenhuth∗and Mara Grunewald†

If bidders consider gains and losses in the context of whether they receive the object or not and

how much they pay separately, the expected revenue is higher in the all-pay auction than in

the first-price auction; if they consider gains and losses over the entire risk-neutral payoff, this

revenue ranking is reversed. In laboratory experiments, we auction money and a real object:

the average revenue is significantly higher in the first-price auction than in the all-pay auction,

suggesting that bidders behave according to wide and not narrow bracketing of gains and losses

in both auction settings.

Key wor ds auction, loss aversion, reference dependence, induced value auction, revenue

equivalence

JEL classification C70, C90, D03, D44, D81

Accepted 29 March2018

1 Introduction

Since Kahneman and Tversky (1979), loss aversion and reference-dependent preferences have been

applied to a variety of empirical and theoretical economic problems. When applying models of loss

aversion, the modeler is required to make an assumption about how individuals evaluate gains

and losses. To illustrate the problem, consider the series of experiments conducted by Kahne-

man et al. (1990), who study the endowment effect in competitive markets. When subjects are

given actual goods (coffee mugs), the endowment effect has an (adverse) impact on trading vol-

umes; if, however, subjects are endowed with money instead, there is no endowment effect present.

The explanation given is that when trading money for coffee mugs, there is a friction caused by

a loss in one (the mug needs to be given up) and a gain (money is received) in the other di-

mension. When money is traded for money, this friction disappears. K¨

oszegi and Rabin (2006)

propose a model which rationalizes the experimental findings mentioned, using the concept of

consumption dimensions, over which individuals have gain–loss utility in an additively separable

manner.

Applying the model of K¨

oszegi and Rabin (2006, 2007), we derive the equilibrium bidding behavior

in the first-price auction (FPA)and in the all-pay auction (APA) for general environments with inde-

∗Epsilon Economics, Chicago, Illinois, USA. Email: reisenhuth@epsiloneconomics.com

†Cologne Institute for Economic Research, Konrad-Adenauer-Ufer 21, 50668 K¨

oln, Germany.

We thank Eddie Dekel, Jeffrey Ely, Armin Falk, Joachim Freyberger, Philipp Kircher, Matthias Kr¨

akel,Henriquede

Oliveira, Jonathan Parker, Ahmad Peivandi, Mikhail Safronov, Alvaro Sandroni,Ron Siegel, Ran Spiegler, Eddie Stein,

and JacquelineWu for advice; we also thank the Bonn Graduate School of Economics and the Center for Economic Theory

at Northwestern University for support and an anonymous referee for important suggestions which have significantly

improved the quality of this article. The views expressed in this article are ours and do not necessarily reflect those of

Epsilon Economics. All errors and omissions are ours.

International Journal of Economic Theory xx (2018) 1–24 © IAET 1

International Journal of Economic Theory

International Journal of Economic Theory 16 (2020) 129–152 © 2019 IAET 129

Auctions with loss-averse bidders Roland Eisenhuth and Mara Grunewald

pendent private values. We study the behavioral implications of loss aversion on bidding strategies,

and compare the revenue across auction formats. In one specification, we consider gains and losses

in two dimensions separately, in the context of whether bidders receive the object or not, and how

much they pay; in the other specification, we consider gains and losses over the entire risk-neutral

payoff, that is, the valuation less the bid. The first specification represents narrow bracketing, while

the second one represents wide bracketing. With wide bracketing, we show that the expectedrevenue

for the auctioneer is higher in the FPA than in the APA, and with narrow bracketing, we show that

the opposite is true.

We conduct laboratory experiments in which either money or a real object is auctioned in both an

FPA and an APA. In both settings, the average revenue is significantly higher in the FPA, suggesting

that bidders may behave according to the one-dimensional model (wide bracketing), despite a real

object being auctioned. Whereas our findings are inconsistent with narrow bracketing, they are

consistent with wide bracketing of gains and losses. Kahneman et al. (1990), however,find ev idence

for loss aversion in exchange markets for coffee mugs, but not when inducedvaluations (tokens) are

exchanged. Hence,their finding s areconsistent with narrow bracketing but not with wide br acketing

of gains and losses.

This paper contributes to the literature on loss aversion and reference-dependent preferences in

several ways. Comparing our results to those in Kahneman et al. (1990), we conclude that whether

individuals apply a narrow or a wide form of bracketing of gains and losses depends on the envi-

ronment under consideration. While competitive markets and auctions are similar in many ways,

there is a lot more uncertainty in present auctions. Additionally,we provide an estimate for the ratio

of marginal disutility of losses to marginal utility of gains of 1.42, using the generalized method of

moments for the data obtained in our experiments. Furthermore, we show that when applying the

K¨

oszegi and Rabin (2007) model, the theoretical predictions crucially depend on the modeler’s deci-

sion about how to define the consumption dimensions over which individuals feel gains and losses.

Finally, our experimental data show that thereis no measur able differencein terms of which auction

generates more revenue between auctioning an actual good and simply money when considering

revenue data alone, as our experiments yield higher revenue in the FPAin both setting s.

Our analysis provides rich insight into bidding behavior and sheds light on the suitability of narrow or

wide bracketing of gains and losses in the K¨

oszegi and Rabin (2006) model for certain environments

and applications. To facilitate the exposition, let θ>0 denote a bidder’s (intrinsic) valuation of the

object being auctioned (θis akin to the marginal utility of consumption of the object in, for instance,

partial equilibrium models). The bidder also pays an amount x≥0 in the auction; this amount may

be only paid upon winning or parting with the object or, in APAs,independent of any possible success

in the auction. In a standard risk-neutral environment, a bidder’s payoffis θ−xwhen winning and

−xwhen losing. The marginal utility of consumption, θ, is thus interpreted as being a dollar figure,

so as to consider the bidder’s net consumer surplus, θ−x, as the bidder’s payoff.

Suppose, for example, that one is interested in studying the effects of risk aversion in independent

private value (IPV) auctions. In this case, the modeler faces the following options:

(i) U(θ−x), where Uis strictly increasing and strictly concave;

(ii) u(θ)+w(−x), where u, w are strictly increasing and strictly concave.

The formulation in (i) is non-separable, and the one in (ii) is additively separable. An interpretation

of the wide bracketing formulation is that bidders are risk-averse over the total consumer surplus,

v−x, obtained in the auction, whereas the interpretation of (ii) is that bidders exhibit risk aversion

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International Journal of Economic Theory 16 (2020) 129–152 2019 IAET

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