Exercise 20.3 [candy-trade-exercise]

Suppose that Ann’s utilities for cherry and lime candies are $c_A$ and $\ell_A$, whereas Bob’s utilities are $c_B$ and $\ell_B$. (But once Ann has unwrapped a piece of candy, Bob won’t buy it.) Presumably, if Bob likes lime candies much more than Ann, it would be wise for Ann to sell her bag of candies once she is sufficiently sure of its lime content. On the other hand, if Ann unwraps too many candies in the process, the bag will be worth less. Discuss the problem of determining the optimal point at which to sell the bag. Determine the expected utility of the optimal procedure, given the prior distribution from Section statistical-learning-section.

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