Kelly Hennigan & Grace Tang
Back to Psych 204b Projects 2010
Background
The winner's curse describes a phenomenon where winners in a common value auction (with an item of fixed but unknown value) tend to pay more than the item is worth. Assuming each bidder has an independent estimate of the value of the item, xi, and these estimates are distributed about the true value with error ε (Fig. 1), the most optimistic estimate will likely be an overestimate. Therefore, if bidders bid at their estimated values, the winner will generally pay more than the true value of the item and incur a net loss.
The optimal bidding strategy to avoid the winner's curse is to adopt the risk-neutral Nash equilibrium (RNNE) strategy, which states that the optimal bid is determined by this equation:
(Under the conditions of the experiment, the Y term is close to zero and is subsequently ignored)
Basically, bidders should adjust their estimates down by the error so that they do not end up paying more than the true value of the item.
However, even when informed of this optimum bidding strategy, bidders continue to bid above the RNNE amount, and end up losing money over many trials because they pay more than the true value of won items.
This suggests that there might be some social value to winning (and social cost of losing).
The utility Ui of the outcome is given by:
where bi is the bid, xo is the value of the item under auction, rwin is the social value associated with winning, and rlose is the social value associated with losing.
Methods
Subjects
Data from 22 individuals was used.
MR acquisition
Data was acquired using 3T Siemens scanner at Baylor College of Medicine in Texas. (TR = 2s)
Auction task
Subjects participated in auctions in groups of 5 or 6, bidding against each other. Each subject was endowed with $30 at the beginning of the session.
The session consisted on 40 auction trials, during which subjects received a personal estimate of the item's value, xi, the error ε, and their current revenue (figure ### ). Pictures of other participants were also displayed on the bottom of the screen.
Subjects entered their bids simultaneously. Individual bids were never revealed to other participants. After all the bids were submitted, the winning bidder was revealed. The winner was shown how much they won or lost, while no information about the true value or money won or lost by the winner was given to the subjects who lost the auction. The winner of each auction round won xo-b, where b was the winning bid for that round, while the other participants won $0.
MR Analysis
Pre-processing
Pre-processing and subsequent analyses were performed using SPM5 (Wellcome Department of Imaging Neuroscience, Institute of Neurology, London, United Kingdom). Images were smoothed with a Gaussian kernel of 4mm full width half maximum
Model fits?
Estimated a GLM with four regressors of interest. The first regressor was included for the time periods regressors for the time periods during which the subject received the outcome of the trial. For trials in which the subject won, monetary outcome was used as a parametric modulator.
Examined -the brain activation associated with the social value of winning/losing the auction (Win>Lose). -correlations between win/loss brain activity and individual estimates of rwin and rlose
Results
... uncorrected for multiple comparisons...
social value of winning/losing in the brain
Figure 1
Fig. 1: Win > Lose contrast
Figure 2
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Fig. 2: Lose > Win contrast
win and lose vs. baseline
Figure X
Figure X: Rwin covariate of beta(win). Note activation of Nucleus Accumbens and visual areas
Figure X
Conclusions
References
McClure, S.M., Van den Bos, W. (in press) The psychology of common value auctions. In Attention and Performance XXIII: Decision Making
van den Bos, W., Li, J., Lau, T., Maskin, E., Cohen, J., Montague, R., et al. (2008). The value of victory: social origins of the winner's curse in common value auctions. Judgment and Decision Making, 3(7), 483-492.