Expected Utility

Expected utility is a measure of the value of an uncertain outcome. It is a generalization of the expected value, which is the average value of an outcome. Expected utility takes into account the decision-maker's attitude towards risk.

The expected value of an outcome is calculated by multiplying the probability of each possible outcome by its value and then summing the products. For example, if there is a 50% chance of winning $100 and a 50% chance of losing $100, the expected value of the outcome is 0.

Expected utility is calculated in a similar way, but it also takes into account the decision-maker's attitude towards risk. This is done by using a utility function, which is a mathematical function that describes how the decision-maker values different outcomes.

There are many different types of utility functions, but one common type is the linear utility function. The linear utility function is a simple function that assigns a value of 0 to the worst possible outcome and a value of 1 to the best possible outcome. The values in between are linearly interpolated.

The expected utility of an outcome is calculated by multiplying the probability of each possible outcome by its utility and then summing the products. For example, if there is a 50% chance of winning $100 and a 50% chance of losing $100, and the decision-maker's utility function is linear, the expected utility of the outcome is 0.5 * 0 + 0.5 * 1 = 0.5.

Expected utility is a useful tool for decision-making under uncertainty. It allows decision-makers to take into account their attitude towards risk when making decisions.