Chapter 17: Principal–Agent Issues and Adverse Selection: Can Everyone Agree?

Chapter 15: Risk Analysis: Walking Through the Fog

where the expected utility of action aj, E(utility aj), equals the summation for all states of nature of the utility associated with the payoff corresponding to action aj and state of nature θi, U(π nature θi occurring, P(θi). ij), multiplied by the probability of state of

After calculating the expected utility, the decision-maker chooses the action with the highest expected utility.

You want to determine whether to expand your business or maintain its current size. The resulting payoff depends on the action you take and whether or not the economy goes into a recession. Figure 15-4 illustrates the resulting payoff matrix with annual profit in millions of dollars. In addition, the payoff matrix includes the utility you associate with each payoff. To use the expected utility criterion, you first determine the probability associated with each state of nature — what happens to the economy. You currently believe the probability that the economy experiences no change is 0.6 and the probability that the economy goes into recession is 0.4.

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Figure 15-4:

Payoff matrix for business expansion.

To determine which action to take based upon the expected utility criterion, you take the following steps:

1. Calculate the expected utility for not expanding.

For each state of nature, multiply the probability of that state of nature by the payoff’s utility given that state of nature and not expanding. Add the resulting values to determine the expected utility.