Anonymity deters collusion in hard-close auctions: experimental evidence

Abstract

This paper studies whether collusion occurs in three-bidder three-object second-price hard-close auctions. The experimental results of two laboratory treatments are reported. The first one, the anonymity treatment, involves subject groups that can trace decisions to the bidder under conditions of anonymity. The second one, the friends treatment, involves groups of subjects who know each other. In this treatment, each bid can be identified with a person. The paper reports no collusion in the anonymity treatment but some collusion in the friends treatment.

Keywords:

• multi-unit auctions
• collusion
• experimental economics

Acknowledgements

We thank Abdolkarim Sadrieh, Katerina Sherstyuk and two anonymous referees for helpful comments. Funding of the experiment by the University of Hannover is gratefully acknowledged.

Notes

1. Examples of design failures included the auction for Australian satellite television licenses (McMillan, 1994) where bids could be withdrawn and the auction for Turkish telecom licenses where a monopoly market resulted from the auction (Klemperer, 2002). As a matter of fact, these design failures induced immediate losses to public households and long-run losses to the domestic customers.

2. In the German Spectrum Auction, Mannesmann used the design to signal T-Mobile a collusive bidding outcome that T-Mobile finally accepted (Grimm et al., 2003; Hoppe et al., 2005).

3. The discrete hard-close auction has also been used in some other recent experimental studies (Ariely et al., 2005; Füllbrunn & Sadrieh 2006). In contrast to these studies, we use a format in which all bids are certainly received by the seller. In electronic real world auctions, there exists the uncertainty that last-minute bids are not received due to bid transmission problems. We do not discuss these problems here (see Roth & Ockenfels, 2002) as they are not part of the auction rules but rather a flaw in their implementation.

4. ( http://pages.ebay.com/help/sell/manage_bidders_ov.html; 30.10.2007)

5. Recent experimental evidence has shown that social ties play a crucial role for cooperation in helping games (Leider et al., 2006) and public goods games (Haan et al., 2006). The cooperation in groups of friends is higher than in anonymous groups. We should expect that collusion among a group of friends is more frequent than in an anonymous group since post-experimental punishment possibilities exist.

6. Neugebauer (2007) shows that bidding above equilibrium results in experimental single-unit sealed-bid auction markets with three anonymous bidders. In contrast, markets with more than seven bidders tend to elicit bidding below equilibrium if no feedback is received on the competitors' bids.

7. The soft-close auction is a dynamic auction with a different termination rule. It terminates as soon as during the final x stages (or minutes) no further bids have been submitted. Conversely, if a new bid has been submitted during the final x stages the auction is prolonged to another x stages. Ex-ante, the stopping time of the game is undetermined, thus the backward induction algorithm cannot be applied. If bidders simultaneously compete in N single-unit markets, a bid submitted in the final x stages prolongs bidding in all markets. Therefore, the threat of reversion to the non-collusive outcome is meaningful in the soft-close auction since the bidders can respond to last stage bids. Brusco & Lopomo (2002) consider such English auctions and derive a perfect Bayes–Nash equilibrium of the signaling game in a private value setting, where bidders split the markets among them. In the two-bidder two-market game, bidders only submit a lowest bid increment ∊ in the market with the higher object valuation. If bids are submitted in separated markets, bidding terminates and (in the limit where ∊ → 0) the bidders receive the maximum buyer surplus in the according market.

8. The same payoffs result if market indices are reversed. In the other cases where both players submit a bid to the same market, mutual sniping is the equilibrium by definition of the collusive strategy.

9. See Füllbrunn (2007) for a detailed discussion.

10. The instructions are appended to the paper.

11. In the experimental instructions, repetitions were called rounds and, on the computer-screen, the current repetition was indicated.

12. The one-tailed Mann-Whitney U-test of the null-hypothesis that the payoff in the anonymity treatment is at least as great as in the friends treatment must be rejected in favor of the alternative that payoff is greater in the friends treatment. The exact p-value is 0.011.

13. The exact p-value of the one-tailed Mann-Whitney U-test is 0.009.

14. The exact p-value of the Wilcoxon test is 0.070. We also conducted the same test for the first eight repetitions and the last eight repetitions (i.e. repetitions 9 to 16) in the experiment, to detect a possible trend. The corresponding p-values are 0.055 (first eight repetitions) and 0.213 (last eight repetitions).

15. The exact p-value is 0.003. Redoing the test for the first and second eight repetitions led to the following p-values; 0.003 (first half), 0.008 (second half).

16. The exact p-value is 0.008. For the first and second eight repetitions the p-values are 0.008 and 0.017.

17. The one-tailed Wilcoxon test yields the same result when we compare the first eight to the last eight repetitions. For the anonymity treatment, the group frequency of efficient auctions is significantly greater in the first than in the last eight repetitions; the exact p-value is 0.026. Conversely, for the friends treatment the p-value is 0.6075.

18. According to the two-tailed Wilcoxon test, the changes in the frequencies of the close-to-equilibrium bids and of the observed below-equilibrium bids is significant between the first and the last eight repetitions; the p-values are 0.0273 and 0.0277.

19. The two-tailed Wilcoxon test that compares the frequency of close-to-equilibrium bids and of below-equilibrium bids between the first and last eight repetitions cannot reject the null hypothesis that no change occurs; the p-values are 0.2402 and 0.2619.

20. The corresponding p-values due to the one-tailed Mann-Whitney U-test of the close-to-equilibrium bids are: 0.0714 for the overall data, 0.1385 for the first eight repetitions, and 0.0362 for the last eight repetitions.

21. The one-tailed Mann-Whitney U-test results of the bid-to-value ratio are as follows. The p-value is 0.0048 for the overall data, 0.0170 for the first eight repetitions and 0.0126 for the last eight repetitions, respectively.