The First-Price Auction Roleplay

A standard trading-desk interview exercise sets up a first-price auction: you and other candidates each submit a single sealed bid for some item — often something with a genuinely uncertain value, like a jar of coins or a made-up asset with a randomly drawn true worth — and whoever bids highest wins it and pays exactly what they bid. It sounds like a simple guessing game, but the setup is chosen deliberately: it's one of the cleanest ways to see, in a few minutes, whether a candidate's trading instincts are sound or whether they'll blow through their edge chasing every win.

Why the naive answer loses money

The tempting move is to estimate the item's value as best you can and bid close to that estimate. But in a first-price auction you pay whatever you bid, and you only win when your bid was the highest of everyone's — which means, on average, you win precisely in the cases where your estimate (or your optimism) ran ahead of everyone else's. If several bidders are estimating the same uncertain value with independent noise, the winning bid tends to come from whoever overestimated the most, not from whoever guessed correctly. Bidding your honest estimate in a first-price auction with a common but uncertain value systematically overpays, because winning itself is bad news about your estimate — this is the same "winner's curse" logic that shows up whenever people bid on something without knowing its exact worth.

What the interviewer is actually watching for

Interviewers running this exercise care less about the exact number you write down and more about the reasoning behind it. Do you shade your bid below your honest estimate, and can you explain why — recognizing that winning at your true estimate would mean you were probably too optimistic? Do you adjust your bid based on how many other bidders are in the room, since more competitors means the eventual winning bid will come from further out on the optimistic tail? Do you stay disciplined if the auction is repeated and you lose several rounds in a row, rather than creeping your bid upward out of frustration to finally "win" one? A candidate who bids sensibly below their estimate, states the reasoning out loud, and holds the line across repeated rounds is demonstrating exactly the instinct a market-maker needs: winning a trade is not automatically good news, and price discipline matters more than the desire to be the one who takes it.

A practical way to answer it

If asked to think through it live, walk through the logic rather than just naming a discount factor: state your best estimate of the value, note that the auction format means you should expect to win only when your estimate was on the high side of the group's true estimates, and explain that shading the bid down protects against that bias — with the amount of shading growing as the number of competing bidders grows, since more bidders means the winning bid is pulled from further into the tail. Getting the exact optimal discount is less important than showing you understand why a discount is needed at all.