Deterring collusion with a reserve price: an auction experiment

Abstract

We experimentally compare collusive behaviors in first-price sealed-bid auctions without and with a reserve price. Before the auction begins, a bidder may offer a bribe to the other bidder, in exchange for a commitment not to participate in the auction. We find that the average offer and the rate of successful bribes are significantly lower in the treatment with a reserve price. These results are largely due to responding bidders who demand a greater share of the benefit from collusion. Although imposing a reserve price reduces efficiency, its optimality and bribe deterrence shift the surplus from the bidders to the seller.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

  1. 1.

    For example, Graham and Marshall (1987) argue that the optimal response of the auctioneer to the formation of coalitions is to establish a reserve price.

  2. 2.

    Gonçalves (2013) offers three alternative explanations for the results: (1) valuations may be private, but correlated; (2) entry may be endogenous; and (3) there may be a common value component in valuations.

  3. 3.

    See Kagel and Levin (2014, Section 4.1), and Correia-da-Silva (2017, Section 3), for surveys.

  4. 4.

    Llorente-Saguer and Zultan (2017) use the same game as in our paper, while Agranov and Yariv (2018) have one treatment with communication and the other with communication and transfer after the auction (no enforceable commitment). In both auction mechanisms, they observe a significant increase in collusion in the latter treatment, as compared to the former.

  5. 5.

    The difference in equilibrium predictions between the two mechanisms arises because bidding the true value is always a weakly dominant strategy for second-price auctions; learning the other bidder’s value does not change the bidding strategy. However, in first-price auctions, the optimal bid depends on the bid of the other bidder. If an equilibrium with positive bribes existed, the responders could infer the proposer’s value from his bribe and bid accordingly. Revealing this information creates an incentive for the proposer to mimic a smaller type (by offering a lower bribe). Therefore, the equilibrium with positive bribes does not exist..

  6. 6.

    Their main focus is to compare the results of first-price and second-price auctions without a reserve price. They observe no significant difference in terms of the levels of collusion. Despite a similar rate of collusion, the first-price auction is less efficient than the second-price auction.

  7. 7.

    This equilibrium also requires the assumption that no player bids above her true value. If this assumption is relaxed, there exist other equilibria. However, we rarely observed such behavior in any treatments. See the further discussion and formal proof in Rachmilevitch (2013a).

  8. 8.

    This equilibrium assumes that after the rejection of a positive bribe, the responder will bid slightly below her value less the bribe and win the item..

  9. 9.

    We randomized a role in each period because of two main reasons. First, this may ensure that each subject understands the information available for each role. Second, it can hinder subjects from maximizing payoffs across periods by using multi-period strategies; for example, a responder may reject the offers in the early periods in the hope to receive better offers in the later periods.

  10. 10.

    The exchange rate at the time of the experiments was about 35 THB/USD, and the minimum wage in Thailand was 300 THB per day.

  11. 11.

    There are two exceptions. First, the average accepted offer amount of cohort 3 in the treatment with a reserve price is greater than that of all other cohorts in both treatments due to an outlier. In this cohort, one subject made sizable offers of 524.8 on average, and hence received large negative payoffs. If we exclude this subject, the average offer amount and the accepted offer amount of this cohort will become 31.7 and 105.3, respectively, in line with other cohorts. Second, the smallest acceptance rate across cohorts in the treatment without a reserve price is exactly equal to the largest one in the treatment with a reserve price.

  12. 12.

    Given our sample size of eight observations in each treatment, the two-sided rank-sum test requires a minimum detectable effect (MDE) of 1.55 for an 80% power and a 5% significant level. Since we already observe larger treatment effects than MDE, we conclude that no additional sample is necessary.

  13. 13.

    In the treatment with a reserve price, a proposer may choose not to make any offer. No offer and an offer of zero have different implications. The former eliminates the possibility that the offer is accepted, while the latter does not. The offer of zero is accepted if the responder’s minimum acceptable offer is zero.

  14. 14.

    If each bidder does not update her belief about the other bidder’s valuation based on the outcome of the bribing stage, the MAO function is then

    $$MAO(v_{i} ) = \left\{ {\begin{array}{*{20}l} {0,} \hfill & {v_{i} \in [0,R)} \hfill \\ {\frac{{v_{i}^{2} }}{2000} - \frac{{R^{2} }}{4000},} \hfill & {v_{i} \in [R,1000]} \hfill \\ \end{array} } \right.$$

    .

  15. 15.

    Risk aversion could also explain overbidding.

  16. 16.

    We also compare the actual and theoretical bids. In the treatment without a reserve price, proposers and responders on average overbid by 45.72 and 20.59, respectively, while in the treatment with a reserve price, these numbers are 47.09 and 31.90. These results confirm our findings in Tables 7 and 8.

  17. 17.

    To calculate the expected payoff in the auction stage, one may use the responders’ actual bids instead of the optimal bids. However, we can observe the responders’ bids only when the offers were rejected. Using the actual bids to calculate the expected payoff results in a larger difference between the average and optimal MAO.

  18. 18.

    In sequential bidding in which the first bidder’s bid may be observed by the second bidder, Fischer et al. (2017) show that the second bidder gains from this leak of information. In our game, we may interpret this as an instance when the proposer partially reveals his value (and potentially his bid) to the responder. This could explain why our mechanism favors the responder.

References

  1. Agranov, M., & Yariv, L. (2018). Collusion through communication in auctions. Games and Economic Behavior,107, 93–108.

    Google Scholar 

  2. Aoyagi, M. (2003). Bid rotation and collusion in repeated auctions. Journal of Economic Theory,112(1), 79–105.

    Google Scholar 

  3. Bajari, P., & Hortaçsu, A. (2003). The winner’s curse, reserve prices, and endogenous entry: Empirical insights from eBay auctions. The Rand Journal of Economics,34, 329–355.

    Google Scholar 

  4. Bajari, P., & Summers, G. (2002). Detecting collusion in procurement auctions. Antitrust Law Journal,70, 143.

    Google Scholar 

  5. Bajari, P., & Ye, L. (2003). Deciding between competition and collusion. Review of Economics and Statistics,85(4), 971–989.

    Google Scholar 

  6. Baldwin, L. H., Marshall, R. C., & Richard, J. F. (1997). Bidder collusion at forest service timber sales. Journal of Political Economy,105(4), 657–699.

    Google Scholar 

  7. Barrymore, N., & Raviv, Y. (2009). The effect of different reserve prices on auction outcomes. Mimeo.

  8. Choi, S., Nesheim, L., & Rasul, I. (2016). Reserve price effects in auctions: Estimates from multiple regression-discontinuity designs. Economic Inquiry,54(1), 294–314.

    Google Scholar 

  9. Correia-da-Silva, J. (2017). A survey on the theory of collusion under adverse selection in auctions and oligopolies. Mimeo.

  10. Cramton, P., & Schwartz, J. A. (2000). Collusive bidding: Lessons from the FCC spectrum auctions. Journal of Regulatory Economics,17(3), 229–252.

    Google Scholar 

  11. Eső, P., & Schummer, J. (2004). Bribing and signaling in second price auctions. Games and Economic Behavior,47(2), 299–324.

    Google Scholar 

  12. Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics,10(2), 171–178.

    Google Scholar 

  13. Fischer, S., Guth, W., Kaplan, T. R., & Zultan, R. I. (2017). Auctions and leaks: A theoretical and experimental investigation. Mimeo.

  14. Gonçalves, R. (2013). Empirical evidence on the impact of reserve prices in English auctions. The Journal of Industrial Economics,61(1), 202–242.

    Google Scholar 

  15. Graham, D. A., & Marshall, R. C. (1987). Collusive bidder behavior at single-object second-price and English auctions. Journal of Political Economy,95(6), 1217–1239.

    Google Scholar 

  16. Greenleaf, E. A., Rao, A. G., & Sinha, A. R. (1993). Guarantees in auctions: The auction house as negotiator and managerial decision maker. Management Science,39(9), 1130–1145.

    Google Scholar 

  17. Hendricks, K., Porter, R., & Tan, G. (2008). Bidding rings and the winner’s curse. The Rand Journal of Economics,39(4), 1018–1041.

    Google Scholar 

  18. Hinloopen, J., & Onderstal, S. (2013). Collusion and the choice of auction: An experimental study. Mimeo.

  19. Hinloopen, J., Onderstal, S., & Treuren, L. (2020). Cartel stability in experimental first-price sealed-bid and English auctions. International Journal of Industrial Organization. https://doi.org/10.1016/j.ijindorg.2020.102642.

    Article  Google Scholar 

  20. Hu, A., Offerman, T., & Onderstal, S. (2011). Fighting collusion in auctions: An experimental investigation. International Journal of Industrial Organization,29(1), 84–96.

    Google Scholar 

  21. Isaac, R. M., & Walker, J. M. (1985). Information and conspiracy in sealed bid auctions. Journal of Economic Behavior & Organization,6(2), 139–159.

    Google Scholar 

  22. Kagel, J. H., & Levin, D. (2014). Auctions: A survey of experimental research. Mimeo.

  23. Klemperer, P. (2002). What really matters in auction design. Journal of Economic Perspectives,16(1), 169–189.

    Google Scholar 

  24. Kwoka, J. E., Jr. (1997). The price effects of bidding conspiracies: Evidence from real estate auction “knockouts”. The Antitrust Bulletin,42(2), 503–516.

    Google Scholar 

  25. Llorente-Saguer, A., & Zultan, R. (2017). Collusion and information revelation in auctions. European Economic Review,95, 84–102.

    Google Scholar 

  26. Lopomo, G., Marx, L. M., & Sun, P. (2011). Bidder collusion at first-price auctions. Review of Economic Design,15(3), 177–211.

    Google Scholar 

  27. Lucking-Reiley, D., Bryan, D., Prasad, N., & Reeves, D. (2007). Pennies from eBay: The determinants of price in online auctions. The Journal of Industrial Economics,55(2), 223–233.

    Google Scholar 

  28. Marshall, R. C., & Marx, L. M. (2007). Bidder collusion. Journal of Economic Theory,133(1), 374–402.

    Google Scholar 

  29. Myerson, R. B. (1981). Optimal auction design. Mathematics of Operations Research,6(1), 58–73.

    Google Scholar 

  30. Noussair, C. N., & Seres, G. (2020). The effect of collusion on efficiency in experimental auctions. Games and Economic Behavior,119, 267–287.

    Google Scholar 

  31. Ostrovsky, M., & Schwarz, M. (2016). Reserve prices in internet advertising auctions: A field experiment. Mimeo.

  32. Phillips, O. R., Menkhaus, D. J., & Coatney, K. T. (2003). Collusive practices in repeated English auctions: Experimental evidence on bidding rings. American Economic Review,93(3), 965–979.

    Google Scholar 

  33. Porter, R. H. (2005). Detecting collusion. Review of Industrial Organization,26(2), 147–167.

    Google Scholar 

  34. Porter, R. H., & Zona, J. D. (1993). Detection of bid rigging in procurement auctions. Journal of Political Economy,101(3), 518–538.

    Google Scholar 

  35. Rachmilevitch, S. (2013a). Bribing in first-price auctions. Games and Economic Behavior,77(1), 214–228.

    Google Scholar 

  36. Rachmilevitch, S. (2013b). Endogenous bid rotation in repeated auctions. Journal of Economic Theory,148(4), 1714–1725.

    Google Scholar 

  37. Rachmilevitch, S. (2015). Bribing in second-price auctions. Games and Economic Behavior,92, 191–205.

    Google Scholar 

  38. Riley, J. G., & Samuelson, W. F. (1981). Optimal auctions. American Economic Review,71, 381–392.

    Google Scholar 

  39. Robinson, M. S. (1985). Collusion and the choice of auction. The Rand Journal of Economics,16(1), 141–145.

    Google Scholar 

  40. Sherstyuk, K. (2002). Collusion in private value ascending price auctions. Journal of Economic Behavior & Organization,48(2), 177–195.

    Google Scholar 

  41. Skrzypacz, A., & Hopenhayn, H. (2004). Tacit collusion in repeated auctions. Journal of Economic Theory,114(1), 153–169.

    Google Scholar 

  42. Trautmann, S. T., & Traxler, C. (2010). Reserve prices as reference points—Evidence from auctions for football players at Hattrick.org. Journal of Economic Psychology,31(2), 230–240.

    Google Scholar 

  43. Troyan, P. (2017). Collusion and signaling in auctions with interdependent values. Journal of Economic Theory,170, 319–345.

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge financial support from the Center for Behavioral and Experimental Economics, Chulalongkorn University. We thank Nartsupon Dumchuen for his helpful research assistance. We benefit from comments by Tim Cason, Ramon Cobo-Reyes, Paan Jindapon, Ragan Petrie, Roberto Weber, two anonymous referees, and seminar participants at the American University of Sharjah; also, by participants in the 2019 Asia-Pacific Economic Science Association Conference, the 2018 Annual Meetings of the Southern Economic Association, the 2017 Asia-Pacific Economic Science Association Conference, and the 4th Joint Workshop between Chulalongkorn University and Osaka University.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ajalavat Viriyavipart.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 53 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sujarittanonta, P., Viriyavipart, A. Deterring collusion with a reserve price: an auction experiment. Exp Econ (2020). https://doi.org/10.1007/s10683-020-09671-x

Download citation

Keywords

  • Collusion
  • Reserve price
  • Auctions
  • Bribes
  • Experiment

JEL Classification

  • D44
  • C91
  • C72