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In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued utility function. The theorems were proved by Gerard Debreu during the 1950s.
Representation theory depends upon the type of algebraic object being represented. There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour. Representation theory depends upon the nature of the vector space on which the algebraic object is represented.
Hartley, however, finds these reasons for representative agent modelling unconvincing. Kirman [2] too, is critical of the representative agent approach in economics. Because representative agent models simply ignore valid aggregation concerns, they sometimes commit the so-called fallacy of composition.
The representation theory of groups divides into subtheories depending on the kind of group being represented. The various theories are quite different in detail, though some basic definitions and concepts are similar.
In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as morphisms between them. . One of the basic thrusts of representation theory is to understand the conditions under which this category is semisimple; i.e., whether an object decomposes into simple objects (see Maschke's theorem for the case of ...
In economics, a utility representation theorem shows that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B.
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes.
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. [1] Social choice studies the behavior of different mathematical procedures ( social welfare functions ) used to combine individual preferences into a coherent whole.