Make a market on two dice

You roll two fair dice privately. The contract pays the sum of the dice. Quote a bid and an offer for it. A counterparty then lifts your offer. What do you do next?

Hint

Fair value is 7. Think about what your width protects you against, and what a trade tells you.

Solution

Quote around fair value, for example 6 / 8. The width pays you for risk (the sum has a standard deviation of about 2.4) and for the chance the other side knows something.

A lifted offer is information. If someone is willing to buy at 8, they may know the sum is high. Move your quotes up, widen them, or reduce size. There is no single right answer, and interviewers care about the reasoning: symmetric around fair value, width tied to risk, and updating after a trade.

Answer

No single number. A sensible quote is 6 / 8, then shift or widen after being lifted.