Painting III

What this auction-game interview question tests

This is a hard statistics and game-theory problem that combines mechanism design with optimal bidding strategy. It's the type of question quant firms use to assess whether candidates can set up and solve a decision problem under incomplete information and strategic competition.

The core challenge is to model the payoff structure correctly: you win only if your bid exceeds both the unknown painting value and your competitor's bid (which depends on that value in a way you must anticipate). Solving it requires you to set up the profit function as a function of your bid choice, account for the probability of winning conditional on the value and your opponent's strategy, and then optimize. The problem rewards careful reasoning about information asymmetry and the interplay between your own uncertainty and your competitor's knowledge.

• Optimal bidding under incomplete information
• Equilibrium analysis in two-player games
• Probability and conditioning on unobserved state variables
• Constrained optimization (finding the bid that maximizes expected profit)