Expected Utility Theory
Introduction
Expected utility theory is a concept in economics and decision theory that plays a crucial role in the rational decision-making process. It is a model of choice under uncertainty that assumes individuals make decisions based on the expected utility, or satisfaction, derived from different outcomes. This theory is a cornerstone of modern economic theory, particularly in the field of microeconomics and game theory.
History and Development
Expected utility theory was first proposed by mathematician Daniel Bernoulli in the 18th century. Bernoulli introduced the concept to resolve the St. Petersburg Paradox, a problem in probability theory that contradicted the expected value theory. Bernoulli's work laid the foundation for the development of expected utility theory, which was later formalized by John von Neumann and Oskar Morgenstern in their book "Theory of Games and Economic Behavior" published in 1944.
Principles of Expected Utility Theory
Expected utility theory is based on several key principles:
Completeness
Completeness refers to the ability of an individual to rank all possible outcomes from most to least preferred. This principle assumes that given any two outcomes, an individual can decide which one they prefer, or if they are indifferent between the two.
Transitivity
Transitivity is the principle that if an individual prefers outcome A over outcome B, and outcome B over outcome C, then they must prefer outcome A over outcome C. This principle ensures consistency in preferences.
Continuity
Continuity assumes that if an individual prefers outcome A over outcome B, and outcome B over outcome C, then there exists a probability mix of outcomes A and C that the individual would be indifferent to outcome B.
Independence
The independence axiom, also known as the substitution principle, assumes that if an individual is indifferent between two outcomes, they should remain indifferent even if a third outcome is mixed in with a certain probability.
Expected Utility Function
The expected utility function is a mathematical representation of an individual's preferences. It assigns a numerical value, or utility, to each possible outcome. The expected utility of a risky prospect is calculated as the sum of the utilities of each outcome, each weighted by its probability of occurrence.
Criticisms and Alternatives to Expected Utility Theory
While expected utility theory is widely used, it has been subject to several criticisms. Some argue that it fails to accurately predict human behavior, as individuals often make decisions that violate the axioms of expected utility theory. This has led to the development of alternative models such as prospect theory and cumulative prospect theory, which attempt to account for observed deviations from expected utility theory.
Applications of Expected Utility Theory
Expected utility theory has wide-ranging applications in various fields. In economics, it is used to model consumer behavior, investment decisions, and insurance purchases. In decision theory, it is used to analyze decisions under uncertainty. In game theory, it is used to predict the strategies of players in a game.
Conclusion
Expected utility theory is a fundamental concept in economics and decision theory. Despite its limitations, it provides a useful framework for understanding and predicting decision-making under uncertainty. By assigning a numerical value to each possible outcome, it allows for a systematic and rational approach to decision-making.