Experiment 10 Auctions
Congratulations, You Overpaid
Bid for an item, reveal everyone’s information, and compare what winning costs under two auction rules.
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Start with “Work It Out, Step by Step” below. The optional expert section explains its symbols as you go. For more examples, use the plain-language math guide.
1. Make a Prediction
Winning Is Only Half the Question
Every bidder submits one hidden bid. The highest bid wins one item. In a first-price auction, the winner pays its own bid. In a second-price auction, the winner pays the second-highest bid. Only the winner pays; everyone else gets zero.
2. Make Your Choice
3. Reveal the Incentives
What Did Everyone Know?
Private value means each bidder knows what the item is worth to that bidder, and those values can differ. Common value means the item has the same actual worth to everyone, but each bidder receives an imperfect estimate. An estimate is a guess based on limited information.
| Bidder | Actual value | Known value or estimate | Bid | Profit |
|---|
The winner’s curse describes the risk that winning a common-value auction selects an unusually optimistic estimate. Paying too much can leave the winner worse off. This is not a claim that every winner loses money.
4. Change One Assumption
Change the Payment Rule or the Information
Bid shading means bidding below your value or estimate to leave room for profit if you win. For instance, 80% of an estimate of 100 gives a bid of 80. The other bidders follow this percentage rule and do not adapt to the auction format.
Model assumptions: private values are whole numbers from 30 to 100. Common values are 50 to 100; each estimate adds an independently drawn error, then stops at zero if necessary. Bids are rounded to whole points. Ties go to the lowest bidder number, and you are bidder 1. There is no minimum sale price or fee to enter. Bidders can afford any permitted bid, and winners cannot sell the item again. The seed is the starting number that reproduces the same random sequence. The comparison uses your percentage rule, not the one manual bid above, and reuses identical items and bids across formats.
Work It Out, Step by Step
Suppose your item value is 80, you bid 70, and the highest other bid is 60.
- Your 70 beats 60, so you win under either rule.
- First price charges your bid of 70. Your profit is \(80-70=10\).
- Second price charges the highest other bid of 60. Your profit is \(80-60=20\).
- If 80 was only your estimate and the actual common value turns out to be 50, the same first-price win loses \(70-50=20\) points.
In words: an item worth 50 minus a payment of 70 leaves a loss of 20. The minus sign before 20 means the final score is below zero. Profit is value received minus the price paid; revenue is the payment the seller receives.
For experts: formal model and assumptions
How to Read the Symbols
- \(h\), \(r\), \(P\), \(v\), and \(u\)
- \(h\) is the highest bid. \(r\) is the second-highest bid, including an equal bid in a tie. \(P\) is the price. \(v\) is the winner’s actual value. \(u\) is the winner’s profit in points. Each letter stands for one number.
In words: first price charges the highest bid; second price charges the next-highest; subtract the payment from the winner’s value. The small words below \(P\) are labels identifying the rule.
In the standard single-item private-value second-price model, bidding your known value is a weakly dominant strategy: it is never worse than another bid against any fixed rival bids, though sometimes several bids give the same result. If the highest rival bid is below your value, winning is useful. If it is above your value, winning loses money. Bidding your value puts the win-or-lose boundary in the right place. This statement assumes points equal value minus price, no extra fees or budget restrictions, and a fixed tie rule.
That argument does not make a raw common-value estimate truthful in the same sense: winning conveys information about how optimistic your estimate was relative to others. The app’s batch comparison holds bidding rules fixed. It does not prove that one format earns a seller more after bidders change their strategies.
See the math reading guide for subscripts, subtraction, and probabilities.
5. Transfer the Lesson
What Is Being Estimated?
You bid for a used machine. Some value comes from how useful it is to your workshop; some depends on hidden wear that matters to every buyer. Which parts are private value and which are common value? What new information would you want before treating a high estimate as a safe bid?
Concept reference: Yale’s lecture on auctions and the winner’s curse.
A Model Is a Place to Start
These small models make the incentives visible. Their results follow from their stated rules; they are not forecasts of how every person or organization behaves. A simulated strategy is a rule, not a personality.
Scenario links save the controls and random seed. To reproduce an interactive run, make the same choices in the same order. Changing a setting restarts the experiment.