Expected utility

Expected utility is a fundamental concept in decision theory and economics that provides a framework for evaluating choices under uncertainty. It is based on the idea that individuals make decisions by considering the potential outcomes of their choices, each associated with its likelihood of occurring, and assigning a utility value to each outcome. Here's a breakdown of the main components of expected utility: 1. **Outcomes**: These are the different possible results of a decision or action.

Optimal decisions refer to choices that yield the best possible outcome or result under a given set of constraints and criteria. These decisions are often made in the context of decision theory, economics, management, and various fields where analysis of alternatives is necessary. The concept is grounded in the idea of maximizing utility, profit, or satisfaction while minimizing costs, risks, or negative outcomes.

Prospect Theory is a behavioral economic theory that describes how individuals make decisions under risk and uncertainty. Developed by psychologists Daniel Kahneman and Amos Tversky in 1979, the theory challenges the traditional utility theory, which assumes that people behave rationally and make decisions solely based on maximizing their expected utility. Key features of Prospect Theory include: 1. **Value Function**: The theory posits that people perceive gains and losses differently.

The term "action axiom" can refer to concepts in different fields, such as philosophy, mathematics, or computer science, but it may not have a specific widely recognized definition across all disciplines. Here are a couple of interpretations based on different contexts: 1. **Philosophical Context**: In philosophy, especially in the study of action theory, an action axiom might refer to basic principles or assumptions about the nature of human actions, intentions, or moral responsibility.

Ambiguity aversion is a concept from behavioral economics that describes the tendency of individuals to prefer known risks over unknown risks. In other words, when faced with choices that involve uncertainty, people often prefer options where they have clear probabilities (known risks) rather than options where probabilities are uncertain or undefined (unknown risks).

The Choquet integral is a mathematical concept used to generalize the idea of integration, particularly in the context of non-additive set functions or capacities. It was named after Gustave Choquet, who introduced it in the context of set theory and probability. The Choquet integral is particularly applicable in situations where the interaction among elements doesn’t behave in an additive manner.

The Expected Utility Hypothesis (EUH) is a fundamental concept in economics and decision theory that describes how rational individuals make choices under conditions of uncertainty. According to this hypothesis, individuals evaluate risky options by considering the expected utility rather than the expected outcome or monetary value alone. **Key Concepts of the Expected Utility Hypothesis:** 1. **Expected Utility**: This refers to the sum of the utilities of all possible outcomes, each weighted by its probability of occurrence.

The expected value, often denoted as \( E(X) \) for a random variable \( X \), is a fundamental concept in probability and statistics that provides a measure of the central tendency of a random variable. It represents the long-term average outcome of a random variable if the process were to be repeated many times.

The Expected Value of Sample Information (EVSI) is a concept used in decision-making and statistics that quantifies the value of obtaining additional information before making a decision. It assesses how much a decision-maker would be willing to pay for the information because it helps in making better decisions. Here's a breakdown of the concept: 1. **Decision Analysis Context**: In situations where decisions are made under uncertainty, having additional information can significantly impact the outcomes. EVSI helps measure that impact.

Generalized Expected Utility (GEU) is an extension of the traditional expected utility theory, which is a cornerstone of decision-making under risk in economics and decision theory. While standard expected utility theory assumes that individuals will make choices to maximize the expected utility based on a given probability distribution of outcomes, GEU accommodates a broader range of preferences and behaviors.

In the context of probability, a lottery refers to a game of chance where players purchase tickets for the opportunity to win prizes based on random draws. The outcome of a lottery is typically determined by a random selection of numbers or symbols, and participants hope that their chosen combinations match those drawn. Key elements of lottery probability include: 1. **Odds**: The chances of winning a prize in a lottery game, often expressed as a ratio (e.g., 1 in X).

Multi-attribute utility (MAU) is a decision-making framework used in various fields such as economics, operations research, and decision analysis to evaluate and compare alternatives based on multiple criteria or attributes. The core idea behind MAU is to assess the preferences of decision-makers regarding different attributes of options they are considering, allowing them to make more informed choices that align with their values and priorities.

Nonlinear expectation is a concept in the field of probability theory and stochastic processes that extends the classical notion of expectation (or expected value) by incorporating nonlinear transformations. It is a part of a broader area known as nonlinear probability, which studies situations where traditional linear assumptions about expectations and probability distributions may not hold. In classical probability, the expectation of a random variable is a linear operator.

Subjective Expected Utility (SEU) is a decision theory framework that combines subjective beliefs about the likelihood of outcomes with utility values assigned to those outcomes. It is an extension of the expected utility theory, which is grounded in objective probabilities. ### Key Components of Subjective Expected Utility: 1. **Subjective Probabilities**: Instead of relying on objective probabilities, SEU allows individuals to use their personal beliefs or subjective judgments to assess the likelihood of different outcomes.

The "uncertainty effect" can refer to different concepts depending on the context—ranging from psychology to economics to physics. Below are a few interpretations based on these fields: 1. **In Psychology**: The uncertainty effect often refers to how individuals react to uncertain outcomes compared to known outcomes, even if the known outcomes are unfavorable. It highlights our tendency to prefer options with certain outcomes over uncertain ones, even if the uncertain option might have a better expected value.