Price a Sequential Four-Box Search Game
WorldquantData Scientist · Technical Screen
Last updated
Four boxes contain one \$100 prize. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.
Price a Sequential Four-Box Search Game
Four boxes contain one $100 prize. Each opening costs the same fee x; you choose an unopened box and may stop after any failure. Find the largest x for which starting optimally has nonnegative expected value. Then, after deriving that break-even fee, decide whether a player who paid that fee for the first opening and failed should continue.
Constraints & Assumptions
- The prize is equally likely in each box.
- Each additional opening costs
x.
Clarifying Questions to Ask
- Should the continuation decision compare only future conditional value and future costs?
- Does finding the prize end the game immediately?
Follow-up questions
- How does the answer generalize to `m` boxes?
- What if unopened boxes have unequal probabilities?
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