Question

4 (a) Explain under what circumstances the 'winners curse' may arise in an auction. (50%)

(b) Discuss whether or not a 'Dutch' auction achieve Pareto efficiency. (50%)

Answer 1

4.a. The winner's curse is a phenomenon that may occur in common value auctions, wherein the winner will tend to overpay due to emotional reasons or incomplete information. Accordingly, the winner will be cursed in one of two ways: either the winning bid will exceed the value of the auctioned asset making the winner worse off in absolute terms, or the value of the asset will be less than the bidder anticipated, so the bidder may garner a net gain but will be worse off than anticipated. However, an actual overpayment will generally occur only if the winner fails to account for the winner's curse when bidding

In a common value auction, the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding.

The winner of an auction is the bidder who submits the highest bid. Since the auctioned item is worth roughly the same to all bidders, they are distinguished only by their respective estimates of the market value. The winner, then, is the bidder making the highest estimate. If we assume that the average bid is accurate, then the highest bidder overestimates the item's value. Thus, the auction's winner is likely to overpay.

More formally, this result is obtained using conditional expectation. We are interested in a bidder's expected value from the auction (the expected value of the item, minus the expected price) conditioned on the assumption that the bidder wins the auction. It turns out that for a bidder's true estimate the expected value is negative, meaning that on average the winning bidder is overpaying.

Savvy bidders will avoid the winner's curse by bid shading, or placing a bid that is below their ex ante estimation of the value of the item for sale—but equal to their ex post belief about the value of the item, given that they win the auction. The key point is that winning the auction is bad news about the value of the item for the winner. It means that he or she was the most optimistic and, if bidders are correct in their estimations on average, that too much was paid. Therefore savvy bidders revise their ex ante estimations downwards to take account of this effect.

The severity of the winner's curse increases with the number of bidders. This is because the more bidders, the more likely it is that some of them have overestimated the auctioned item's value. In technical terms, the winner's expected estimate is the value of the n^th order statistic, which increases as the number of bidders increases. In other words, more bidders = higher winner's curse.

There is often confusion that the winner's curse applies to the winners of all auctions. However, it is worth repeating here that for auctions with private value (i.e. when the item is desired independent of its value in the market), winner's curse does not arise. Similarly, there may be occasions when the average bid is too low relative to exterior market conditions e.g. a dealer recognizing an antique or other collectible as highly saleable elsewhere when other bidders do not have the necessary expertise.

The winner’s curse happens because the auction winner tends to be the bidder that overestimates value.

A simple game will illustrate. Imagine an economics professor auctions off a jar of coins to a classroom. The rules are that students must guess the value of the coins, and the professor will sell the jar to the highest bidder. What can we expect out of this auction?

The student guesses will be distributed in some fashion. If students are guessing honestly, typically the average of the guesses will be very close to the true value of the coins. Averaging the guesses will average out errors and exhibit the phenomenon dubbed “the wisdom of crowds.”

This turns out to be bad news for the auction winner. If the average guess is close to the true value of the coins, then the highest guess must be larger. The winner of the auction will be the student that overestimated the jar of coins and he will lose money on average.

b. A Dutch auction is a public offering auction structure in which the price of the offering is set after taking in all bids to determine the highest price at which the total offering can be sold. In this type of auction, investors place a bid for the amount they are willing to buy in terms of quantity and price.

A Dutch auction also refers to a type of auction in which the price on an item is lowered until it gets a bid. The first bid made is the winning bid and results in a sale, assuming that the price is above the reserve price. This is in contrast to typical options, where the price rises as bidders compete.

Pareto efficiency: – the item must sell to the buyer with the highest valuation of the item.

Pareto-efficiency means that there's no way to reallocate goods and make everyone better off. This is a weak notion of efficiency in general. For example, suppose we cannot require payments, and just have to allocate a single good to someone. Then, if you give the good to anyone, that would be Pareto-efficient.

English auction with no reserve price must be efficient since, if a buyer with a low valuation was about to buy, the highest valuation buyer would bid higher.

English auction with a reserve price need not be efficient since if the reserve price is set above the (unknown to the seller) highest buyer valuation valuation, then there will be no sale and so no gains‐to‐trade.

Dutch auction need not be efficient. No buyer knows other buyers’ valuations, so the highest valuation buyer may delay too long and lose to another bidder.