Dueling Stock II

What this probability and valuation interview question tests

This is a medium-difficulty probability question that combines conditional expectation with financial valuation reasoning. It asks you to work backwards from a constraint (zero-sum market structure) to infer prices when an outcome occurs that wasn't explicitly specified in the problem setup.

The core skill is recognizing that in a consistent probability model, you must use the law of total expectation across all possible outcomes to determine what happens in the case where both companies succeed simultaneously. You'll need to set up equations that respect the zero-sum property and the given payoff structure for other scenarios, then solve for the missing piece.

• Conditional probability and scenario analysis
• Expectation and backward induction
• Constraint-based reasoning in pricing problems
• Market consistency and arbitrage-free conditions