Debreu's Theorems are a set of preference representation theorems in economics and decision theory, showing conditions under which an individual's ranked preferences over a set of options can be represented by a real-valued utility function whose ordering of any two options matches the individual's own ranking. Proved by Gerard Debreu during the 1950s, they underlie the standard practice of modeling rational choice and games using ordinary numerical payoff functions.
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StatementDebreu's theorems are preference representation theorems, statements about how a preference ordering can be represented by a real-valued utility function. 1 Classification
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Source Debreu's representation theorems (Wikipedia)
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Source Debreu's representation theorems (Wikipedia)
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1. Debreu's representation theorems (Wikipedia)
Lead section
In economics, the Debreu's theorems are preference representation theorems-statements about the representation of a preference ordering by a real-valued utility function.
Existence of ordinal utility function section, opening sentence
The 1954 Theorems say, roughly, that every preference relation which is complete, transitive and continuous, can be represented by a continuous ordinal utility function.
In Branch: Game Theory, Lead
In economics, the Debreu's theorems are preference representation theorems-statements about the representation of a preference ordering by a real-valued utility function.
In Group: Economic Theory, Lead paragraph
In economics, the Debreu's theorems are preference representation theorems-statements about the representation of a preference ordering by a real-valued utility function.
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