Uncertain Utilities

The utility may be uncertain and risky. In this case, the effective utility matrix is a probability weighted average.

Let p₁ be the probability of an utility in state 1. Let p₂ be the probability of an utility in state 2 where p₁ + p₂ = 1

Then

U_ij = p₁(U_ij)₁ + p₂(U_ij)₂

is the effective utility.