Abstract
The lack of a behavioral isomorphism between theoretically equivalent auction institutions is a robust finding in experimental economics. Using a near-continuous time environment and graphically adjustable bid functions, we are able to provide subjects with extensive feedback in multiple auction formats. We find that (1) First Price and Dutch Clock auctions are behaviorally isomorphic and (2) Second Price and English Clock auctions are behaviorally isomorphic. We further replicate the established result (1) that prices in Dutch Clock auctions exceed those of English Clock auctions and (2) that prices in First Price auctions exceed those of Second Price auctions. The latter pattern is often attributed to risk aversion which changes the equilibrium bidding strategy for First Price and Dutch Clock auctions. Because we observe each participant’s bid function directly, we find evidence suggesting a different explanation, namely that bidders are best responding to the distribution of observed prices.
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Notes
There have been some previous experiments that solicited bid functions. For example, Kirchkamp et al. (2009) asked subjects provide bids for six possible value realizations and then linearly imputed bids for other values.
Davis and Korenok (2009) show that such near-continuous time experiments enable subjects to gain considerable experience which leads to behavioral outcomes that are consistent with competitive predictions even when more standard experimental approaches (with less feedback and experience) do not.
Perhaps the most common theoretical explanation for the observed price differences between first price and second price sealed bid auctions and between Dutch Clock and English clock auctions is that bidders are risk averse (see Cox et al. 1982). Other explanations for over bidding relative to the risk neutral equilibrium predictions for first price auctions include a flat maximum critique (Harrison 1989), winner regret (Engelbrecht-Wiggans 1989) convex probability weighting (Goeree et al. 2002), learning models (Ockenfels and Selten 2005; Neugebauer and Selten 2006), and loser regret (Englerbrecht-Wiggans and Katok 2008).
For a recent review of Dutch Clock auction experiments see Adam et al. (2017).
The instructions are provided in an online appendix on the journal’s website.
Twelve auctions were conducted in the typical manner so that on average each subject would win four auctions.
Using the difference between the average earnings of males and females within a group of N = 4 bidders, a sign test fails to reject the null hypothesis that males and females earned the same amount in treatments involving the Second Price and English auctions (p = 1.000). Males, however, earn more in the treatments involving First Price and Dutch auctions (p = 0.012).
For the Dutch auction this expectation assumes risk neutral bidders following the equilibrium bid function.
This pattern would be surprising if the similarity in prices between theoretically equivalent formats was due to the near-continuous time nature of the environment making the clock less salient.
When using all of the near-continuous auction data the p values are 0.246 and 0.313, respectively, for the Wilcoxon signed rank tests.
When using all of the near-continuous data the p values are less than 0.001, for each of the pairwise Wilcoxon rank sum tests.
Our use of the last 50 periods here and elsewhere in the paper is arbitrary. The qualitative results are robust to other durations.
Averages are taken for each value from 0 to 10 in 0.1 increments.
Specifically, we assume that utility is represented by U(x) = xr.
Best responses to observed distribution of prices yields discontinuous best response curves because of the discrete nature of realized prices.
While Fig. 4 is suggestive, this explanation was developed ex-post. Because our experiment was not designed to test this idea, we leave doing so to future research.
The difference between a subject’s bid in the Dutch and First Price auction was regressed on a constant term. Similarly, the difference between a subject’s bid in the English and Second Price auction was regressed on a constant term. Figure 6 plots the p values associated with these constants.
The software forced the subjects to place a bid of zero when the value was 0.
Care should be taken when considering regression results as the tests are not independent across values since they are based on the same bid function. This is why the p values are continuous.
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Acknowledgements
We thank Jeff Kirchner for brilliantly programming the software, Megan Luetje for recruiting the participants, Chapman University for funding the participant payments, and feedback from James Cox, participants at the Economic Science Association meetings, the editor and two anonymous reviewers.
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Deck, C., Wilson, B.J. Auctions in near-continuous time. Exp Econ 23, 110–126 (2020). https://doi.org/10.1007/s10683-019-09603-4
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DOI: https://doi.org/10.1007/s10683-019-09603-4