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.
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Notes
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.
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.
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.
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..
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.
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).
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..
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.
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.
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.
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.
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.
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
$$MAO(v_{i} ) = \left\{ {\begin{array}{*{20}l} {0,} \hfill & {v_{i} \in [0,R)} \hfill \\ {\frac{{v_{i}^{2} }}{2000} - \frac{{R^{2} }}{4000},} \hfill & {v_{i} \in [R,1000]} \hfill \\ \end{array} } \right.$$.
Risk aversion could also explain overbidding.
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.
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.
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.
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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.
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Sujarittanonta, P., Viriyavipart, A. Deterring collusion with a reserve price: an auction experiment. Exp Econ 24, 536–557 (2021). https://doi.org/10.1007/s10683-020-09671-x
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DOI: https://doi.org/10.1007/s10683-020-09671-x