Auction Mechanism Generator
A sealed second-price auction has a startling property: bidding your true value is the best you can do, whatever anyone else does. In a first-price auction it never is, so everyone shades their bid and the winner depends on who guessed best. This generates private values, runs both formats, and proves the second-price claim by enumerating every alternative bid the winner could have made.
What this generator does
Gives each bidder a private value, computes the equilibrium shaded bid for a first-price auction, and runs both formats. The truthfulness of the second-price format is then checked by enumerating every alternative bid the winner could have submitted.
How to use this tool
- Choose how many bidders.
- Generate, and read each bidder's private value and shaded first-price bid.
- Compare who wins and what they pay under each format.
- Note that the second-price winner pays the runner-up's value, not their own.
Understanding the controls
- How many bidders
- Between 2 and 6, each with a private value they alone know. More bidders push the shaded bids closer to true values, which is why competition raises revenue.
- Seed
- Reproduces the same private values, so the two formats can be compared on identical input.
Common use cases
- Teaching why second-price auctions are truthful and first-price ones are not
- Comparing auction formats on identical private values
- Producing worked examples for a mechanism design course
- Showing why bid shading is rational rather than dishonest
- Generating auction scenarios with a provable dominant strategy
How this generator works
In the first-price auction the winner pays their own bid, so bidding your value earns nothing and everyone shades below it — the symmetric equilibrium shades by a factor of one minus one over the number of bidders. In the second-price auction the winner pays the runner-up's value, which severs the link between your bid and your price and makes honesty dominant. That claim is not merely asserted: every alternative bid is tried, and none earns the winner more surplus than bidding their true value.
Randomness and fairness
Uses your browser's cryptographic random source for the private values by default. A seed switches to a reproducible sequence, deterministic and not cryptographically secure.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Values are independent and private, which is the standard textbook setting; common-value auctions bring in the winner's curse and behave differently.
- The first-price shading formula assumes all bidders are symmetric and rational, which real bidders are not.
- Only single-item auctions are covered — combinatorial auctions over several items are a much harder problem.
- Reserve prices, entry fees and collusion are all outside the model.
Privacy and your data
Values and outcomes are generated in your browser and never transmitted, stored or included in analytics.
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