<p>Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility functions like quadratic, exponential or logarithmic etc</p>

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2021-09-15T07:39:04.213Z
"*Von Neuman-Morgenstern utility theorem apply only to linear utility functions*" This seems to be covered in the [statement of the theorem](https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem#The_theorem). Can you explain what your exact question is?
Giskard
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2021-09-15T08:08:21.463Z
@Giskard so the whole game theory is based only in linear programming problems? What about utility functions that are concave and increasing?
Nav89
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2021-09-15T08:21:54.843Z
I am not sure you understand what the Von Neuman-Morgenstern utility theorem is about.
Giskard
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2021-09-15T08:22:37.863Z
As an aside, pre Nash game theory was indeed mostly linear programming.
Giskard
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2021-09-15T08:25:33.320Z
@Giskard ok can we clarify then what is it about the VNM theorem and then talk about the the pre Nash and after Nash game theory?
Nav89
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2021-09-15T09:58:37.220Z
Yes, can you please clarify what your question is? That would be lovely.
Giskard
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2021-09-15T10:16:14.017Z
vNM utility functions are linear *in probabilities*. Bernoulli utility functions of risk-neutral agents are linear *in wealth*.
VARulle
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2021-09-15T12:37:52.923Z
@Giskard i will verify the question
Nav89
<microeconomics><mathematical-economics><utility><expected-utility>
Von Neuman-Morgenstern utility theorem apply only to linear utility functions?
Nav89
# Von Neuman-Morgenstern utility theorem apply only to linear utility functions?

(Asked by: username_0 on 2021-09-15)

Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility functions like quadratic, exponential or logarithmic etc

**Tags:** microeconomics, mathematical-economics, utility, expected-utility

> **Comments:**
> **username_1**: "*Von Neuman-Morgenstern utility theorem apply only to linear utility functions*" This seems to be covered in the [statement of the theorem](https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem#The_theorem). Can you explain what your exact question is?  
> **username_0**: @username_1 so the whole game theory is based only in linear programming problems? What about utility functions that are concave and increasing?  
> **username_1**: I am not sure you understand what the Von Neuman-Morgenstern utility theorem is about.  
> **username_1**: As an aside, pre Nash game theory was indeed mostly linear programming.  
> **username_0**: @username_1 ok can we clarify then what is it about the VNM theorem and then talk about the the pre Nash and after Nash game theory?  
> **username_1**: Yes, can you please clarify what your question is? That would be lovely.  
> **username_2**: vNM utility functions are linear *in probabilities*. Bernoulli utility functions of risk-neutral agents are linear *in wealth*.  
> **username_0**: @username_1 i will verify the question  

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## 0 answers

