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Anscombe-Aumann Subjective Expected Utility Model
In decision theory, the Anscombe-Aumann subjective expected utility model (also known as Anscombe-Aumann framework, Anscombe-Aumann approach, or Anscombe-Aumann representation theorem) is a framework to formalizing subjective expected utility (SEU) developed by Frank Anscombe and Robert Aumann. Anscombe and Aumann's approach can be seen as an extension of Savage's subjective expected utility model, Savage's framework to deal with more general acts, leading to a simplification of Savage's representation theorem. It can also be described as a middle-course theory that deals with both objective uncertainty (as in the von Neumann-Morgenstern utility theorem, von Neumann-Morgenstern framework) and subjective uncertainty (as in Savage's framework). The Anscombe-Aumann framework builds upon previous work by Leonard J. Savage, Savage, John von Neumann, von Neumann, and Oskar Morgenstern, Morgenstern on the theory of choice under uncertainty and the formalization of SEU. It has since become ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, rationally under uncertainty. It differs from the Cognitive science, cognitive and Behavioural sciences, behavioral sciences in that it is mainly Prescriptive economics, prescriptive and concerned with identifying optimal decision, optimal decisions for a rational agent, rather than Descriptive economics, describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by Social science, social scientists, as it lays the foundations to Mathematical model, mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science. History The roots of decision theory lie in probability theory, developed by Blai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called scalar (mathematics), ''scalars''. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field (mathematics), field. Vector spaces generalize Euclidean vectors, which allow modeling of Physical quantity, physical quantities (such as forces and velocity) that have not only a Magnitude (mathematics), magnitude, but also a Orientation (geometry), direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix (mathematics), matrices, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Choice Modelling
Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) in order to infer positions of the items (A, B and C) on some relevant latent scale (typically "utility" in economics and various related fields). Indeed many alternative models exist in econometrics, marketing, sociometrics and other fields, including utility maximization, optimization applied to consumer theory, and a plethora of other identification strategies which may be more or less accurate depending on the data, sample, hypothesis and the particular decision being modelled. In addition, choice modelling is regarded as the most suitable method for estimating consumers' willingness to pay for quality improvements in multiple dimensions. Related terms There are a number of terms which are considered to be synonyms with the term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude. For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, rationally under uncertainty. It differs from the Cognitive science, cognitive and Behavioural sciences, behavioral sciences in that it is mainly Prescriptive economics, prescriptive and concerned with identifying optimal decision, optimal decisions for a rational agent, rather than Descriptive economics, describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by Social science, social scientists, as it lays the foundations to Mathematical model, mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science. History The roots of decision theory lie in probability theory, developed by Blai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Transformation
In Euclidean geometry, an affine transformation or affinity (from the Latin, '' affinis'', "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. If is the point set of an affine space, then every affine transformation on can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Up To
Two Mathematical object, mathematical objects and are called "equal up to an equivalence relation " * if and are related by , that is, * if holds, that is, * if the equivalence classes of and with respect to are equal. This figure of speech is mostly used in connection with expressions derived from equality, such as uniqueness or count. For example, " is unique up to " means that all objects under consideration are in the same equivalence class with respect to the relation . Moreover, the equivalence relation is often designated rather implicitly by a generating condition or transformation. For example, the statement "an integer's prime factorization is unique up to ordering" is a concise way to say that any two lists of prime factors of a given integer are equivalent with respect to the relation that relates two lists if one can be obtained by reordering (permutation, permuting) the other. As another example, the statement "the solution to an indefinite integral is , up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triviality (mathematics)
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple object possessing a given structure (e.g., group (mathematics), group, topological space). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval Trivium (education), trivium curriculum, which distinguishes from the more difficult quadrivium curriculum. The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove. Triviality does not have a rigorous definition in mathematics. It is Subjectivity and objectivity (philosophy), subjective, and often determined in a given situation by the knowledge and experience of those considering the case. Trivial and nontrivial solutions In mathematics, the term "trivial" is ofte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a binary relation on a set (mathematics), set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Every partial order and every equivalence relation is transitive. For example, less than and equality (mathematics), equality among real numbers are both transitive: If and then ; and if and then . Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy is also an ancestor of Carrie. On the other hand, "is the birth mother of" is not a transitive relation, because if Alice is the birth mother of Brenda, and Brenda is the birth mother of Claire, then it does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility Maximization Problem
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of Optimal decision, optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a Natural borrowing limit, constraint on total spending (income), the prices of the goods and their Preference (economics), preferences. Utility maximization is an important concept in consumer theory as it shows how consumers decide to allocate their income. Because consumers are modelled as being Rational choice theory, rational, they seek to extract the most benefit for themselves. However, due to bounded rationality and other biases, consumers sometimes pick bundles that do not necessarily maximize their utility. The utility maximization bundle of the consumer is also not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility Hypothesis
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude. For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lottery
A lottery (or lotto) is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. The most common regulations are prohibition of sale to minors and licensing of ticket vendors. Although lotteries were common in the United States and some other countries during the 19th century, by the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in the U.S. and most of Europe as well as many other countries. This remained so until well after World War II. In the 1960s, casinos and lotteries began to re-appear throughout the world as a means for governments to raise revenue without raising taxes. Lotteries come in many formats. For example, the prize can be a fixed amount of cash or goods. In this format, there is risk to the org ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
