Many decision problems have the following simple structure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c is incurred. If decision 2 is made, there are two possible outcomes, with costs c1 and c2 and probabilities p and 1 - p. We assume that c1 < c < c2. The idea is that decision 1, the riskless decision, has a moderate cost, whereas decision 2, the risky decision, has a low cost c1 or a high cost c2.
a. Find the decision maker’s cost table, that is, the cost for each possible decision and each possible outcome.
b. Calculate the expected cost from the risky decision.
c. List as many scenarios as you can think of that have this structure. (Here’s an example to get you started. Think of insurance, where you pay a sure premium to avoid a large possible loss.)
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