Expected Utility

Most states are not certain, may only occur with some probability. Hence if we can calculate utility and probability, we can find Expected Utility of the state:

$$\begin{array}{rl}E[U(s1)]& =\text{probability}(s1).\text{utility}(s1)\end{array}$$

For $S$ (set of states), and where $\sum (sϵS)$ indicates the sum over all states in $S$:

$$E[U(S)]=\sum (sϵS)\text{Prob}(\text{state}=s)\ast \text{utility}(s)$$

We run into issues with utilities such as:

• summing up over all states might be very costly in terms of processing resource / time
• not always straightforward to calculate the utility
• difficult to have a long term view