Abstract
The total revenue from an “all-pay contest” is the sum of expenditures from all individual players, so it is important to ask whether it increases with the number of actual players—which is our definition of competition. This is the first paper to use field data to study this question empirically. Using novel instrumental variables, we document strong empirical evidence that the revenue of a penny auction—which is a form of all-pay contest that recently emerged on the Internet—increases with the number of bidders. Our findings cast doubt on the standard model of all-pay contests that presumes that all bidders are fully informed.
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Notes
In an all-pay auction, all bidders must pay whether they win or lose, and the winner is the bidder who bids the most. Because each player in such auctions has the incentive to outbid her competitors by only a small amount, pure strategies typically have no equilibrium. In mixed-strategy Nash equilibria, players are just indifferent as to whether to participate, so the total revenue equals the common value of the prize (Baye et al. 1996; Bulow and Klemperer 1999).
Win or lose, all bidders in a penny auction must pay, so it is an all-pay game or all-pay contest. The winner of a penny auction is the last bidder, who is often not the one who submitted the largest number of bids, so a penny auction is not an all-pay auction, in which the winner must be the bidder who submits the largest aggregate bid.
By November 2010, at least 125 penny auction websites targeting US consumers were being monitored by Compete.com (a web traffic monitoring company). According to its data, in November 2010 the total number of unique monthly visitors to these penny auction websites reached 25.1 percent of that to eBay but has since declined sharply. Unlike eBay, penny auction websites sell products themselves. See Wang and Xu (2013) for more details.
There is one exception: The value of bid tokens bought through the BIN option in token auctions is less than $0.75 because of a usage restriction that was imposed on such bid tokens. We assume that the value of a token bought through the BIN option is 0.8 × $0.75. See Wang and Xu (2013) for more details.
If all players are rational and fully informed, the net revenue of a penny auction should be zero—i.e., the absolute revenue equals the value of the item—regardless of the number of bidders who exercise the BIN option. See Sect. 4 for more explanations.
Auction revenue may depend on the number of bidders in some special cases. For example, the probability that an auction does not start at all may depend on the number of bidders. The greater is the number of bidders, the more likely is the auction to start. Another example is that there may exist some equilibria in which the revenue is strictly lower than the value of the object and the likelihood of obtaining such equilibria depends on the number of bidders.
Hinnosaar (2013) makes the alternative assumption that simultaneous bidders all incur a bid cost. In practice, tying does not occur because time is continuous.
With the BIN option, it is difficult to characterize the equilibrium because of a complication that arises when a bidder’s total number of bids in an auction reaches the level at which she is better off by exercising the BIN option than by not doing so. At that point, a bidder’s marginal cost of an additional bid is zero because an additional bid automatically reduces the additional cost she needs to pay to exercise the BIN option. Therefore, a rational bidder may adopt the strategy of always bidding until her total cost of bids reaches the value of the auctioned product.
Bidders may suffer from various behavioral biases (e.g., the sunk cost fallacy) that lead them to overbid.
Recall that BigDeal typically released an auction with an initial countdown clock that would last for 36 h, and the 30-s timer did not start until only 30 seconds was left on the initial countdown clock. Since nearly all bids at BigDeal were placed after the 30-second timer started, what affected the auction outcome was the point at which the 30-second timer started, not the initial 36-hour countdown clock.
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Acknowledgments
We are especially grateful to the editor for many suggestions that significantly improved the paper. We also thank two anonymous referees, Ian Gale, and seminar participants at George Washington University, Tsinghua University, Central University of Finance and Economics, and Zhejiang University for helpful comments. We acknowledge financial support from Resources for the Future and Beijing Normal University. Any remaining errors are ours only.
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Wang, Z., Xu, M. Empirical Evidence on Competition and Revenue in an All-Pay Contest. Rev Ind Organ 49, 429–448 (2016). https://doi.org/10.1007/s11151-016-9511-6
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DOI: https://doi.org/10.1007/s11151-016-9511-6