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What this optimal-strategy information-theory question tests

This is a medium-difficulty probability and game theory question that asks you to prove a lower bound on expected cost and determine uniqueness of the optimal strategy. It tests whether you can reason about decision trees, information theory, and the fundamental limits of search under uncertainty.

To solve problems like this, candidates typically set up the expected cost recursively (or via decision-tree analysis), show that any strategy must satisfy a lower bound derived from information-theoretic principles, and then verify whether that bound can be achieved by more than one decision rule. The question rewards rigorous proof over intuition alone.

• Decision trees and branching complexity
• Expected cost under adversarial feedback
• Information-theoretic lower bounds
• Uniqueness of optimal solutions