0
$\begingroup$

This is the definition of an expected utility function that I'm working with:

The utility function $U:\mathcal{L}\to\mathbb{R}$ has an expected utility form if there is an assignment of numbers $(u_{1},...,u_{N})$ to the $N$ outcomes $\{\omega_{1},...,\omega_{N}\}$, such that the following is satisfied for any simple lottery $L=(\omega_{1},...,\omega_{N};p_{1},...,p_{N})\in\mathcal{L}$: \begin{equation}\label{eq:vnm} U(L)=\sum_{i=1}^{N}p_{i}u_{i}. \end{equation} My question: Is it true that the assignment of numbers $(u_{1},...,u_{N})$ are given by the Bernoulli function $u:\Omega\to\mathbb{R}$, where $\Omega$ denotes the sample space. And is it true that $U(L):\mathcal{L}\to\mathbb{R}$ is called the Von Neumann-Morgenstern expected utility function, where $\mathcal{L}$ denotes the set of simple lotteries?

$\endgroup$
1
$\begingroup$

That's true, but it should be constructed the other way round: The assignment of numbers $u_i$ to outcomes is not given by the Bernoulli utility function but defines it. The terminology of Bernoulli and Von Neumann-Morgenstern utility functions is common, but not universally used in the context of EUT.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.