# Decision Theory - Under Risk

Risk – is defined as hazard or chance of loss even disaster. Thus, in decision making under risk, the decision maker is exposed to some chances of injury or loss. In such circumstances, the decision maker then must first assess the degree and the probability of such loss or failure.

Tools/Criterion of Analysis in Making Decision:

1. Expected Monetary Value (EMV or EV)

Using a decision table with conditional values (payoffs) that are monetary values, and probability assessments we can determine the expected monetary value (EMV) for all alternatives. EMV is the sum of possible payoffs of the alternatives, each are weighted by the probability of the payoff occurring. Thus –

EMV (alternative i) = (payoff of first state of nature) x (probability of first state of nature) + (payoff of second state of nature) x (probability of second state of nature)

+…+ (payoff of last state of nature) x (probability of last state of nature)

The alternative with the maximum EMV is then chosen.

THIS THEN IS THE EXPECTED VALUE WITHOUT PERFECT INFORMATION.

2. Expected Value of Perfect Information (EVPI)

The expected value with perfect information is the expected or average return, in the long run, if we have perfect information before a decision has to be made. Step 1: To calculate this, we will pick the best alternative for all state of nature then multiply its payoff by the probability of occurrence of that state of nature. Thus,

Expected value with perfect information (EVwPI) -Step 1 = (best payoff or consequence for first state of nature) x (probability of first state of nature) + (best payoff for second state of nature) x (probability of second state of nature) +…+ (best payoff for last state of nature) x (probability of last state of nature).

Step 2 - The EVPI is the expected outcome with perfect information minus the expected outcome without perfect information or the...

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