Expected Utility Theory (EUT) emerged from the efforts of Daniel Bernoulli in the 18th century to solve the St. Petersburg paradox. Later, John von Neumann and Oskar Morgenstern formalized the concept in their 1944 book “Theory of Games and Economic Behavior”. This theory has since become fundamental in economics, finance, and decision theory.
Types/Categories
- Normative EUT: Provides guidelines on how decisions should be made to be rational.
- Descriptive EUT: Describes how decisions are actually made by individuals in practice.
Key Events
- 1738: Daniel Bernoulli proposes the concept to solve the St. Petersburg paradox.
- 1944: Von Neumann and Morgenstern formalize EUT in “Theory of Games and Economic Behavior”.
Detailed Explanations
Expected Utility Theory posits that when faced with uncertainty, individuals make decisions by considering the expected utility of outcomes, rather than the expected monetary value. The theory assumes individuals are rational and have consistent preferences.
Mathematical Formulation
The expected utility \(EU\) of an outcome is calculated as:
- \(p_i\) is the probability of outcome \(i\),
- \(u(x_i)\) is the utility of outcome \(i\).
Example Calculation
If an individual faces a gamble with two possible outcomes: $100 (with probability 0.5) and $50 (with probability 0.5), and their utility function \(u(x) = \sqrt{x}\), the expected utility would be:
Charts and Diagrams
graph TD
A[Start]
B{Decision Node}
C[Outcome 1: $100, u($100)]
D[Outcome 2: $50, u($50)]
A --> B
B --> C
B --> D
Importance and Applicability
EUT is crucial in various fields:
- Economics: For understanding consumer choices and market behavior.
- Finance: In portfolio optimization and risk assessment.
- Insurance: In pricing and designing insurance products.
- Behavioral Science: To study deviations from rational decision-making.
Examples
- Insurance Purchase: A person decides to buy insurance by evaluating the expected utility of being insured versus uninsured.
- Investment Decisions: An investor chooses a portfolio by balancing risk and expected returns to maximize utility.
Considerations
- Risk Aversion: Individuals often exhibit risk aversion, which EUT can model by incorporating concave utility functions.
- Realism: While EUT assumes rationality, real-world decisions often deviate due to bounded rationality and behavioral biases.
Related Terms with Definitions
- Risk Aversion: Preference for certain outcomes over uncertain ones with the same expected value.
- Prospect Theory: An alternative to EUT, emphasizing how people perceive gains and losses.
Comparisons
- EUT vs. Prospect Theory: While EUT focuses on expected outcomes based on utilities, Prospect Theory accounts for psychological biases and irrational behaviors.
Interesting Facts
- Bernoulli’s Contribution: Daniel Bernoulli’s work laid the foundation for both modern utility theory and risk analysis.
- Applications in AI: EUT principles are applied in artificial intelligence for decision-making algorithms.
Inspirational Stories
- Pioneers’ Journey: The collaboration between von Neumann and Morgenstern, merging insights from economics and mathematics, revolutionized decision theory and game theory.
Famous Quotes
- John von Neumann: “There’s no sense in being precise when you don’t even know what you’re talking about.”
Proverbs and Clichés
- “Better safe than sorry”: Reflects risk aversion in decision-making.
Jargon and Slang
- “Utility Maximizer”: A term for someone who makes decisions to maximize their utility.
FAQs
Q: What is Expected Utility Theory? A: EUT is a theory modeling decision-making under uncertainty by considering the expected outcomes of different choices.
Q: Why is EUT important? A: It helps understand and predict choices in economics, finance, and other fields where uncertainty is a factor.
Q: How does EUT model risk aversion? A: By using concave utility functions to reflect the diminishing marginal utility of wealth.
References
- Bernoulli, Daniel. “Exposition of a New Theory on the Measurement of Risk.” 1738.
- Von Neumann, John, and Oskar Morgenstern. “Theory of Games and Economic Behavior.” 1944.
Summary
Expected Utility Theory is a cornerstone of modern decision theory, providing a framework for making rational choices under uncertainty. It incorporates probabilities and utilities to evaluate different outcomes, with wide-ranging applications in economics, finance, and beyond. Through its mathematical formulation and assumptions, EUT continues to influence how we understand and model decision-making behavior.
