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The Dollar Auction Game: A Laboratory Comparison Between Individuals and Groups

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Abstract

The aim of this paper is to analyze bidders’ behavior, comparing individuals and groups’ decisions within the dollar auction framework. This game induces subjects to fall prey into the paradigm of escalation, which is driven by agents’ commitment to higher and higher bids. Whenever each participant commits himself to a bid, the lower bidder, motivated by the wish to win as well as to defend his prior investment, finds it in his best interest to place a higher bid to overcome his opponent. The latter mechanism may lead subjects to overbid. We find that the Nash equilibrium of the game is only rarely attained. Second, we detect clean evidence that groups’ decisions are, on average, superior to individuals’ decisions. Learning over time is clearly evident, leading individuals to perform nearly as good as groups in the final rounds of the game.

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Notes

  1. Comprehensive surveys comparing group and individual decision-making can be found in Charness and Sutter (2012) and Temerario (2014).

  2. eBay auctions, mineral right auctions and corporate takeovers are widespread examples.

  3. See Arkes and Blumer (1985).

  4. While in the easy level of the task the majority of subjects can solve the problem, in the difficult version only a minority can succeed.

  5. O’Neill et al. (2015) showed that “Face-to-face teams were more effective on all decision”.

  6. During the experiment only group’s members can look at each other in the eye, and on the group’s screen, but they cannot look at other groups’ screen or other participant in the lab.

  7. The ECU (Experimental Currency Unit) is the currency used in the experiment.

  8. Of course, since there were no upper limits to bidding, subjects could potentially suffer massive losses. To mitigate this downside, subjects were previously involved in another experiment where they could only make a gain. After the two experiments, no subject ended up with a negative net profit.

  9. While our partner design presents several upsides (e.g. in terms of providing multiple independent observations within a session), it may result in reputational effects and cooperation. For instance, subjects might alternate who bids the minimum and who does not. We control for this through a fixed effects logit model testing whether winning at t − 1 affects the probability of winning in t. No evidence of strategic cooperation is detected in both treatments, with the lagged binary variable (win_t − 1 exhibiting a coefficient of 0.55 and a p value of 0.128 in the individual treatment and a coefficient of 0.22 and a p value of 0.546 in the group treatment).

  10. Since subjects in a $-auction experiment can loose money we run this experiment coupled with a public good game with strictly positive pay-off. In order to avoid wealth effects subjects did not received any feedback on their pay-off or other subjects’ contribution to the public good. The public good part lasted approximately 30 min and subjects earned 25 €.

  11. This evidence is largely supported in the related literature. See, for example, Blinder and Morgan (2005).

  12. Indeed, within dyad observations over time are likely to be more correlated than between dyad observations.

  13. Starting from a pilot sample of 8 independent observations (dyads) per treatment, a power sample size (PSS) analysis led us to engage a sample of 20 independent observations in each condition, whose size ensured a power greater than 0.98 in the one sample mean tests and greater than 0.77 in the two sample mean tests. Details are available upon request.

  14. Individual Losers: N = 20, t = 6.81, p = 0.00; Individual Winners: N = 20, t = 7.66, p = 0.00; Group Losers: N = 20, t = 4.33, p = 0.00; Group Winners: N = 20, t = 5.10, p = 0.00).

  15. While inexperienced individuals present an expected RMSE of 12.07, inexperienced groups exhibit an expected RMSE of around 4.

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Funding

Funding was provided by Università degli Studi di Bari Aldo Moro (IT) (Progetto Idea).

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Authors and Affiliations

  1. Dipartimento di Economia, Management e Diritto dell’Impresa, Università degli Studi di Bari “Aldo Moro”, Bari, Italy

    Andrea Morone, Simone Nuzzo & Rocco Caferra

Authors
  1. Andrea Morone
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  2. Simone Nuzzo
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  3. Rocco Caferra
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Corresponding author

Correspondence to Andrea Morone.

Appendices

Appendix A

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figure b
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Appendix B

See Tables 2 and 3.

Table 2 Mann–Whitney U test
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Table 3 Mann–Whitney U test
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Appendix C

See Table 4.

Table 4 Mann–Whitney U test
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Appendix D

Period by period comparison between actual and simulated groups’ bids for losers. See Tables 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14.

Table 5 Comparison between actual and simulated groups’ bids for losers in period 1
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Table 6 Comparison between actual and simulated groups’ bids for losers in period 2
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Table 7 Comparison between actual and simulated groups’ bids for losers in period 3
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Table 8 Comparison between actual and simulated groups’ bids for losers in period 4
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Table 9 Comparison between actual and simulated groups’ bids for losers in period 5
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Table 10 Comparison between actual and simulated groups’ bids for losers in period 6
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Table 11 Comparison between actual and simulated groups’ bids for losers in period 7
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Table 12 Comparison between actual and simulated groups’ bids for losers in period 8
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Table 13 Comparison between actual and simulated groups’ bids for losers in period 9
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Table 14 Comparison between actual and simulated groups’ bids for losers in period 10
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Appendix E

Period by period comparison between actual and simulated groups’ bids for winners. See Tables 15, 16, 17, 18, 19, 20, 21, 22, 23 and 24.

Table 15 Period by period comparison between actual and simulated groups’ bids for winners in period 1
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Table 16 Period by period comparison between actual and simulated groups’ bids for winners in period 2
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Table 17 Period by period comparison between actual and simulated groups’ bids for winners in period 3
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Table 18 Period by period comparison between actual and simulated groups’ bids for winners in period 4
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Table 19 Period by period comparison between actual and simulated groups’ bids for winners in period 5
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Table 20 Period by period comparison between actual and simulated groups’ bids for winners in period 6
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Table 21 Period by period comparison between actual and simulated groups’ bids for winners in period 7
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Table 22 Period by period comparison between actual and simulated groups’ bids for winners in period 8
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Table 23 Period by period comparison between actual and simulated groups’ bids for winners in period 9
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Table 24 Period by period comparison between actual and simulated groups’ bids for winners in period 10
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Morone, A., Nuzzo, S. & Caferra, R. The Dollar Auction Game: A Laboratory Comparison Between Individuals and Groups. Group Decis Negot 28, 79–98 (2019). https://doi.org/10.1007/s10726-018-9595-5

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