Point72 Quantitative Researcher Intern Interview Experience — Auction Theory and a 32-Ball Tournament Puzzle

Hiring process: five rounds total. This was round one.

Behavioral

• Self-introduction
• Why do you want to do quant?
• Share the trading strategies you know
• Talk about your previous relevant internship experience

Math questions

Question 1: Second-price auction

Two people are bidding on an item.

Rules:

• Whoever bids the highest gets the item.
• The winner doesn't pay their own bid — they pay the other bidder's bid (this is a second-price auction, aka a Vickrey auction).

Given:

• Your valuation of the item is v, where 0 < v < 1.
• Your opponent's valuation is uniformly distributed on [0,1].

Question: What's your optimal bidding strategy?

Answer: The optimal strategy is to bid your true valuation, i.e. b(v) = v.

Why: Bidding above your valuation only increases your risk of loss. Bidding below your valuation risks missing out on a deal that would've been profitable. In a second-price auction, truthful bidding is a dominant strategy.

Follow-up: Is this statistical arbitrage or pure arbitrage?

Answer: Pure arbitrage. Because the strategy doesn't depend on any probabilistic forecasting — truthful bidding is strictly optimal no matter what the opponent bids.

Extension: The interviewer then asked — if this were a first-price auction instead, how would the optimal strategy change?

Question 2: 32 balls

There are 32 balls, all with different weights. You can only compare the weight of two balls at a time.

Part 1: How many comparisons do you need to find the heaviest ball?

Answer: 31. Because finding the max requires n-1 = 32-1 = 31 comparisons.

Part 2: How many comparisons do you need to find the second-heaviest ball?

Answer: 35.

Approach: First run a tournament (elimination bracket) to find the maximum, which takes 31 comparisons. The eventual winner, along its path through the bracket, beat log2(32) = 5 other balls. The second-heaviest ball has to be one of those 5 balls that lost only to the winner. Finding the max among those 5 takes 4 more comparisons. 31 + 4 = 35.

Overall, this round's math questions were mainly testing:

• Auction theory (second-price auctions, strategy-proofness)
• Game theory (dominant strategy)
• Tournament trees
• Comparison models
• Optimal algorithmic complexity

Compared to traditional probability questions, this leaned more toward combining algorithms with economic theory.