Kelly Hennigan & Grace Tang

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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, x_i, 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).

To account for these social factors in the bidding process, the utility U_i of the outcome can be given by:

where b_i is the bid, x_o is the value of the item under auction, r_win is the social value associated with winning, and r_lose 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, x_i, 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 x_o-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 during which participants were shown the estimate and error information and making their bids. Two regressors for the time periods during which the subject received the outcome of the trial were also included, one for trials when the subject won, and another for when the subject lost. For trials in which the subject won, monetary outcome was used as a parametric modulator, giving rise to the final regressor. Six regressors of no interest were included for motion.

We 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 r_win and r_lose

Results

... uncorrected for multiple comparisons...

social value of winning/losing in the brain

Figure 1: Win > Lose Contrast

File:Win-lose rev.png Fig1a: Look at that brain on fire!

File:Win-lose2 rev.png Another screen shot

Fig. 1: Win > Lose contrast

Figure 2: Lose > Win Contrast

Fig 2a: Parietal Activation

Fig 2b: Mystery Region

win and lose vs. baseline

Figure 3: Win > Mean activity

File:Rwin nacc rev.jpg Xa: NAcc

File:Rwin vis rev.png Xb: Visual

Figure 4: Lose > mean BOLD activity

File:Rlose CAUD rev.png Fig 2a: Caudate Activation

File:RloseINS rev.png Fig 2a: Insula Activation

File:Rlose VIS rev.png Fig 2b: Enhanced Activation in Visual Regions

Figure X

File:Rwin nacc rev.jpg

Figure X: Rwin covariate of beta(win). Note activation of Nucleus Accumbens

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.