Maths in economics, finance and society · Ambitious · Dissertation

Which auction raises the most?: a maths EPQ idea

Why it works as an EPQ

A famous theorem says they raise the same on average under some conditions. You can test what happens when the conditions fail.

Scope and difficulty

Ambitious. Ambitious. Two bidders and uniform values by hand; more by simulation.

The maths

Builds on these A Level topics: Probability · Integration · Statistical distributions.

You would learn:

• Bidding strategies
• Expected revenue with continuous distributions
• Revenue equivalence

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Find the best bids in each auction for two bidders with uniform values.
2. Calculate expected revenue in each.
3. Simulate with more bidders and different value distributions.
4. Judge which design an auctioneer should choose and when.

Pitfalls

• Assuming bidders behave as the model says without discussion.
• Errors in integrals of order statistics.

Where to start reading

• Search for: revenue equivalence theorem two bidders uniform
• Search for: second price auction dominant strategy

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in economics, finance and society ideas · all 93 ideas

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