Question

Suppose that we have two copies of Intermediate Microeconomics to sell to three (enthusiastic) students. How can we use a sealed-bid auction that will guarantee that the bidders with the two highest values get the books?

Short answer

Use a sealed-bid second-price auction where each wins pays the highest losing bid.

Step-by-step solution

Understanding Sealed-Bid Auction

In a sealed-bid auction, bidders submit one bid each without knowing the other bidders' bids. Each bid reflects the student's maximum willingness to pay for a copy of the book.

Setting Up the Auction Rules

Establish that each student submits a single bid for one copy of 'Intermediate Microeconomics.' The two highest bids will win, with each winner paying the amount of the third highest bid (or the highest losing bid). This variant is known as a Vickrey auction or second-price auction.

Analyzing Bidder Strategy

In a second-price auction, the optimal strategy for each bidder is to bid their true valuation of the item. This is because if they bid lower, they risk losing even if they would have won, and if they bid higher, they don't pay more due to the nature of the second-price system.

Determining Winners and Prices

After all bids are submitted, sort the bids from highest to lowest. The top two bids win the books. Each winning bidder pays the amount of the third highest (losing) bid, ensuring the mechanism favors those with the highest true valuations.

Example Scenario

Imagine Student A bids $50, Student B bids $70, and Student C bids $60. The two highest bidders are B and C. Student B and Student C each pay $50, the third-highest bid, for their copies of the book.

Key concepts

Intermediate Microeconomics

Intermediate Microeconomics involves examining how consumers and firms make decisions to allocate their resources, especially in scenarios involving market mechanisms and auctions. Understanding these concepts is crucial when studying auctions as they often involve strategic decision-making and resource allocation. In the context of an auction for a textbook like 'Intermediate Microeconomics', students must decide how much they value the book and what they are willing to pay.
These decisions are influenced by their understanding of economic principles such as utility, demand, and opportunity cost. Intermediate Microeconomics serves as a foundation for understanding auction strategies and predicting outcomes due to its exploration of supply and demand dynamics. With this knowledge, students can apply theories when participating in, for example, a Vickrey auction for textbooks.

Vickrey Auction

A Vickrey auction is a special type of sealed-bid auction where the highest bidder wins, but pays the second-highest bid. It is named after William Vickrey, a Canadian economist who introduced this concept. This auction format encourages bidders to submit bids equal to their true valuation of the item because they know they won’t have to pay their bid amount, but rather the second-highest bid.
This method is intriguing as it reveals the true value bidders place on an item without incentivizing them to overbid. It’s a clever way to ensure the items go to the individuals who value them the most, enhancing economic efficiency. In the exercise, the books are awarded to the two top bidders, but they only pay the amount of the third-highest bid. This auction type diminishes the winner's curse effect and creates a fair bidding environment.

Bidder Strategy

Determining the right bidder strategy is crucial when participating in a second-price auction like the Vickrey auction. Unlike other auction types where you may try to guess or influence the bids of others, the best strategy here is straightforward: disclose your true valuation of the item via your bid.
If you undervalue what you bid, you risk losing the opportunity to win even if your true valuation would have won. Overstating your bid doesn't increase your payment if you win, because you only pay the second-highest bid. This bid strategy simplifies decision-making. It relies less on speculation about others’ bids and more on genuine valuations, which can make the process more transparent and fairer from a strategic perspective.

Second-Price Auction

In a second-price auction, the highest bidder wins but pays the amount of the second-highest bid, also known as a Vickrey auction in sealed-bid form. This auction type is designed to encourage honesty among bidders because the price paid isn’t based on the winner's bid but on what the competition bid—the next closest offer.
This auction form is unique as it eliminates the need for bid shading or estimating competitors' bids, which can be common in first-price auctions. It aligns with economic efficiency by ensuring the item is awarded to the bidder who values it most without causing them to overpay. An excellent example of a second-price auction is provided in the textbook solution, where the two winners end up paying the third-highest bid, which protects them from overpaying while ensuring fairness. This encourages transparency and fair competition.