The Winner's Curse
Regardless of whether there is a first price auction or second auction (Vickery Auction), in the real world, bidders often have incomplete information. Because of the discrepancy of information, they may either overbid or the value of the thing they were bidding on is actually worth less than expected. In both ways, the winner overpays for the item suffers a loss. Hence, if bidders keep the winner’s curse in mind when they bid, they will not overpay for the item by slightly shading their bids.
It is said that the first instance that the winner’s curse was brought up was by researchers for the petroleum industry in the 1950s. In fact, in 1971 employees at ARCO noticed that oil companies bidding on offshore drilling rights (first-price auctions) were receiving relatively low returns on their investments. They often found that there were a lot less oil underground than initially thought. The winner’s curse is also frequently used in studies done on baseball contracts. Researchers were investigating the relationship between the value of the player versus his potential performance.
The winner’s curse is rooted in a decision maker’s failure to take into account all the information when making a decision. In some cases this is because they don’t know the actual value of the item. As a result, they have to make the best guess at the true value of the item. The winner of the auction is the highest bidder (at first price or second price based on auction) and will slightly overvalue the asset. So, although the winner “wins,” he or she actually suffers a net lost. Furthermore, as more and more bidders become involved, the winner’s curse becomes even more pronounced since the winner has to outbid even more competitors. In other words, as there are more bidders, the distribution of their bids become more spread out and thus the value the winner bids is farther away from the true value.
The concept of the winner’s curse can also be explained through these following examples
Imagine you have a 2 gallon water jug filled with pennies, totally up to $30. Bidders, not knowing the true value of the jug bid for it. They have no other information except that they know how large the container is. Then, bidders, one after another, bid for the jug. It is safe to assume that the more bidders we have, the closer to a bell shaped curve with the average bid being around $30 (wisdom of crowds) if they truly guess how much the jug is worth. However, regardless of the auction being first or second price, the winner will over pay for the jug.
When bidding on a smaller item, bidders may forget to take into account of shipping. As a result, they will overpay for the item because of the additional cost.
In an initial public offering, it is difficult to predict whether the business in question will raise the price of the stock beyond the original price. In this instance, bidders need to carefully evaluate what the future value of the company or suffer a loss. Clearly, if the company doesn't fare well (winner overvalued the stock), the price of its stocks will decrease and the purchaser will lose money.
Implications and Strategy
The winner’s curse is not necessarily a negative thing. If bidders take into account that
- They do not have all the information about competitors
- Do not have all the information about item
- There may be multiple bidders
Because of the reasons above bidders may be likely shade their bid. The more bidders that are involved, the more likely a bidder is going to hedge his or her bet. If everyone hedges their bids, because they have taken into account the winner’s curse, they will be able to avoid the imminent loss of revenue. In this case, it is better to not win the bid than to lose money.
In the case with 1st price auctions, the optimal strategy is to shade your bid in order to receive a payoff. The more you shade you bids, the larger the payoff. However, the trade-off is that a lower bet will result in a lower probability of winning. If you bid too high, you won't receive that much payoff in the case that you do win. But, once you taken the Winner's Curse into consideration, it is profitable to shade your bets even more because of the uncertainty in information.
For 2nd price auctions, the optimal strategy is to bid your true value as discussed in the textbook. If you overbid your valuation, you will have a negative payoff and if you underbid your valuation, you would not win the auction. However, with the presence of Winner's Curse, there might just be too much uncertainty for there to be too much competition. Hence, shading your bid will allow you to live in the lower part of the bid dispersion with less demand. However, as shown earlier, if there was a lot of competition, you would still be better off at not losing money by shading your bid.