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Debreu theorems : ウィキペディア英語版
Debreu theorems

In economics, the Debreu theorems are several statements about the representation of a preference ordering by a real-valued function. The theorems were proved by Gerard Debreu during the 1950's.
== Background ==
Suppose we interrogate a person and ask him questions of the form "Do you prefer A or B?" (when A,B can be options, actions to take, states of the world, consumption bundles, etc.). We write down all the answers. Then, we want to represent the preferences of that person by a numeric ''utility function'', such that the utility of option A is larger than option B if and only if the agent prefers A to B.
The Debreu theorems come to answer the following basic question: what conditions on the preference relation of the agent guarantee that we can find such representative utility function?

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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