Question

A game theorist fills a jar with pennies and auctions it off on the first day of class using an English auction. Is this a private-value or a common-value auction? Do you think the winning bidder usually makes a profit?

Short answer

This is a common-value auction. The winning bidder usually does not make a profit due to the 'winner's curse'.

Step-by-step solution

Identify the Type of Auction

The English auction is a type of auction where the price is incrementally increased until no higher bids are made. The highest bidder wins. In this problem, a jar filled with pennies is auctioned off in this manner. We first need to determine if this auction is common-value or private-value.

Define Common-Value Auctions

Common-value auctions involve items where the value is identical for everyone but is unknown at the time of the auction. Each bidder estimates the item's value based on the same information, and the true value is revealed after the auction.

Define Private-Value Auctions

Private-value auctions consist of items that hold different values for different bidders. Each bidder knows their own valuation before the auction, and valuations are independent of each other.

Classify the Auction

In this auction, the value of the jar filled with pennies is the same for everyone, based on the total amount of money that it holds. Thus, it is a common-value auction, since the exact monetary value is the same for all and is unknown until the pennies are counted.

Evaluate Profit Likelihood for the Winning Bidder

In common-value auctions, especially with inexperienced bidders, the winner often overestimates the true value of the auctioned item, leading to the 'winner's curse' where the winning bid exceeds the actual value. Unless the bidder has precise knowledge of the jar's content or underestimates the value, it is unlikely they will make a profit.

Key concepts

English Auction

An English auction is one of the most common and straightforward auction formats. In its simplest form, the auctioneer starts with a low bid price and invites participants to bid higher amounts. Bidding continues until no one is willing to place a higher bid. The highest bidder at the end of this process wins the auction.
This type of auction is highly dynamic as it allows bidders to strategically place their bids while observing the behavior of other participants. This live interaction means that the auction is transparent, with all bidders aware of the current highest bid.
As a result, English auctions often lead to competitive bidding, driving the item’s price up until it reaches its market value or higher. This open and ascending price auction style is advantageous when selling items that benefit from competitive interest to maximize sale price.
Some key aspects of an English auction include:

• Bidding starts low and progresses upwards.
• The auction ends when no higher bid is placed.
• Bidders have full visibility of the highest bid at any time, which can influence their bidding strategy.
• It encourages competition, potentially leading to a higher selling price for the auctioneer.

Common-Value Auction

In a common-value auction, the item on sale has a value that is identical for all bidders, but this value is not known precisely during the bidding process. Each bidder makes their estimation of this common value based on limited information. Once the auction is concluded, the actual value becomes known, and it is this true value that matters to the winner.
A classic example is an auctioning off an oil field, where all bidders use geological reports to guess the amount of oil available, but the exact quantity is revealed only after the purchase. As in the exercise, auctioning a jar of pennies is a common-value auction since the exact value is the same for everyone but unknown until counted.
This auction type can lead to a phenomenon known as the 'winner's curse.' The winner's curse occurs when the auction winner realizes afterward that they have overpaid for the item because their estimate was too optimistic compared to the true value. To avoid this, experienced bidders will often bid conservatively, taking into account the possibility of overestimation.
Key points of common-value auctions include:

• All bidders have the same end value in mind for the item post-auction.
• The true value of the item is unknown at the time of bidding.
• There is a risk of overbidding due to incorrect valuation, leading to the winner's curse.

Private-Value Auction

A private-value auction is different from a common-value auction. In this scenario, an item's value is subjective and can differ from one bidder to another. Each bidder knows what the item is worth to them personally before the auction begins.
Examples of private-value auctions include art pieces, antique furniture, or collectibles, where personal tastes and preferences heavily influence one's willingness to bid. The value arises not from the objective worth but from the individual significance placed on the item by each participant.
Here, each bidder's valuation is independent, meaning what one person is willing to pay does not affect another's valuation. This independence allows participants to craft their bidding strategy based on personal needs and desires rather than attempting to guess a universal value.
Important aspects of private-value auctions are:

• The item's value varies by bidder.
• Each participant knows their desired valuation before bidding.
• Valuations are independent from one another, creating unique bidding conditions.
• Bidding is usually based on personal demand or taste.