definition
staged
Von Neumann Morgenstern Axioms
For preferences over lotteries, the vNM axioms require the ordinary preference axioms together with lottery-specific compatibility conditions.
The central lottery-specific axioms are:
- independence: mixing both sides with the same third lottery preserves preference;
- continuity: if $L_1$ is weakly preferred to $L_2$ and $L_2$ is weakly preferred to $L_3$, then $L_2$ is indifferent to a mixture of $L_1$ and $L_3$.
Together with completeness and transitivity, these axioms are the input for the expected-utility representation theorem.
References
- [MSZ, Chapter 2, Axioms 2.12-2.17] Maschler, Solan, and Zamir, Game Theory. The vNM axioms for preferences over lotteries.