Painting II

What this optimal-bidding interview question tests

This is a medium-difficulty decision-theory problem that combines uniform probability distributions with expected-value maximization. Quant firms use questions like this to assess whether a candidate can model an asymmetric payoff structure and optimize under uncertainty.

The core challenge is recognizing that your payoff depends on the relationship between your bid and the unknown true value, and that higher bids increase your win probability but only when you overpay. You'll need to set up the expected profit as a function of your bid, then find the bid that maximizes it. The solution requires careful handling of the conditional probability that your bid exceeds the true value, combined with the specific payoff terms.

• Expected value under uniform distributions
• Optimization of piecewise payoff functions
• Win probability and adverse selection logic