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Debreu's Theorems

Game Theory

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.

Facts
Statement
Debreu's theorems are preference representation theorems, statements about how a preference ordering can be represented by a real-valued utility function. 1
Proof Year
1954 1
Classification
Statement Form
Existence Theorem 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Debreu's representation theorems (Wikipedia)
  • Lead section, first sentence
    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.
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