expectedutility

Expected utility is a concept in decision theory that describes how rational agents make choices under conditions of uncertainty. It posits that an agent will choose the option that maximizes their expected utility, which is calculated by considering the possible outcomes of each choice, the probability of each outcome occurring, and the utility (or value) the agent assigns to each outcome.

The formula for expected utility is the sum of the product of the utility of each outcome and its probability. For example, if a choice has two possible outcomes, A and B, with probabilities P(A) and P(B) respectively, and the agent's utilities for these outcomes are U(A) and U(B), then the expected utility of the choice is E = P(A) * U(A) + P(B) * U(B).

The concept of utility itself is subjective and represents an individual's preference for different states of the world. It is not necessarily equivalent to monetary value. For instance, a person might derive more utility from avoiding a small financial loss than they would from gaining the same amount of money, demonstrating risk aversion. Conversely, a risk-seeking individual might be willing to accept a higher probability of a negative outcome for the chance of a significantly larger positive outcome.

Expected utility theory provides a normative framework for how decisions should be made to be consistent with rational preferences. It has applications in economics, finance, psychology, and artificial intelligence, helping to model and predict behavior in situations where outcomes are not certain. Deviations from expected utility maximization are often studied in behavioral economics, highlighting systematic biases in human decision-making.