353.Bidding for the Car
★★★optimal stoppingJane Street
A car's value is uniformly distributed between 0 and 1000, and you do not know it. You submit a sealed bid; if your bid is at least the car's value you buy it at your bid price, and you can then resell it for 1.5 times its actual value. If your bid is below the value, nothing happens. What bid maximises your expected profit?
Sign in to submit an answer and track it toward your stats.
Sign inHint
Winning is itself bad news about the value. Work out the expected value of the car conditional on your bid having won, not its unconditional average.
Want timed drills, mental math, and a market-making game too? Try the full practice suite →