Experiment 20 Mechanism Design
Write the Rules
Allocate one scarce item by queue, lottery, reported priority, or auction and test the rewards for exaggerating.
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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. Predict, Then Submit Your Report
Who Gets the One Available Item?
You, B, and C want one item. Each person has an actual value: how many points the item is worth to them. A declared value is the number they tell the organizer. The rule sees declarations, not actual values. The sandbox shows actual values to you as an observer so you can inspect the result.
A mechanism is a set of rules for collecting choices, assigning the item, and deciding payments. Select one below, then choose what to report. B’s and C’s reports stay fixed when the app compares your chosen report with your actual value.
2. Reveal the Incentives
Compare the Result With Reporting Your Actual Value
| Person | Actual value | Declared value | Gets item? | Payment | Waiting cost | Personal score |
|---|
3. Change One Assumption
Change the Value, the Reports, or the Rule
- Queue: your selected arrival place matters; reports do not. B arrives before C among the remaining places. Arriving first costs 2 waiting points, second costs 1, and third costs zero. Everyone pays their waiting cost, including those who miss the item.
- Lottery: each person has a 1 in 3 chance, regardless of reports. A seed is a number that lets the program repeat the same random sequence.
- Reported priority: the largest report gets the item free. Actual need is not verified. This is a rule based on a claim, not an ethical ranking of real needs.
- Second-price auction: the largest report wins, but the winner pays the second-largest report. Others pay nothing. This assumes people can afford the payment and care about actual value minus payment.
- Ties: priority and auction ties use the fixed order You, then B, then C. That order is chosen before reports and never changes with their size.
Try actual value 7 and report 11 with B reporting 10. Compare reported priority with the auction. Then make your report 7 again.
Work It Out, Step by Step
- The item is worth 7 points to you. B reports 10.
- Under free reported priority, reporting 11 gets you the item and a score of 7. Reporting 7 loses and gives you zero. This rule can reward exaggeration.
- In the second-price auction, reporting 11 still wins, but you pay 10. Your score is negative 3.
- Reporting your actual value of 7 loses the auction and gives you zero, which is better than losing 3 points.
- If the item were worth 12 to you instead, winning for 10 would give you 2. Reporting 12 would win without guessing a larger number.
In words: subtract the price from the actual value, not from the report. Money paid to the organizer remains inside our group total. Waiting costs are spent effort and are removed from that total.
For experts: formal model and assumptions
When Truthful Reporting Is Safe
Incentive compatibility means the rule makes reporting actual information a best choice under its assumptions. In this one-item second-price auction, bidding actual value is a weakly dominant strategy: for each fixed set of other bids, it is at least as good as any different bid. “Weakly” allows ties; an inaccurate report can sometimes give the same score.
- \(v, p, u\)In words: actual value, price, and personal score.
- These letters label three amounts. When you win, subtract p from v to get u. When you lose the auction, your score is zero.
If the highest other report is below your actual value, winning at that price helps. If it is above your value, winning hurts. Reporting actual value separates those cases. At equality, winning and losing both give zero. The fixed tie rule does not change the argument.
The claim assumes one item, private values that do not change with others’ information, no bid fees, enforceable payments, no budget limits, no collusion, and value-minus-payment preferences. A private value is a value known to its owner. Collusion means participants coordinate their reports to change the outcome. This lab does not model either shared uncertain values or coordinated bids.
The lottery has an exact expected personal score of actual value divided by three. The batch button simulates 600 draws for illustration; its frequency counts can differ from exactly 200 each. Reporting cannot change the lottery chances or the queue position.
For more examples of the notation, use the math reading guide.
4. Transfer the Lesson
One Shared Appointment
A team has one specialist appointment available. Would a queue, a lottery, or a claim of greatest need produce the same behavior? What information and goals would you need before deciding whether payments are appropriate?
Compare your reasoning
A queue can reward costly early arrival. A lottery gives equal chances but may miss the person who values the appointment most. Unverified priority claims can reward exaggeration. An auction adds affordability and payment assumptions that may not fit the setting. Decide what you are trying to achieve before choosing the rule.
Concept reference: Tim Roughgarden’s Stanford lecture, Mechanism Design Basics.
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.