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von Neumann-Morgenstern Utility


Definition: von Neumann-Morgenstern utility describes a utility function (or perhaps a broader class of preference relations) that has the expected utility property: the agent is indifferent between receiving a given bundle or a gamble with the same expected value.

There may be other, or somewhat stronger or weaker assumptions in the vNM phrasing but this is a basic and important one. It does not seem to be the case that such a utility representation is required to be increasing in all arguments or concave in all arguments, although these are also common assumptions about utility functions. The name refers to John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior. Kreps (1990), p 76, says that this kind of utility function predates that work substantially, and was used in the 1700s by Daniel Bernoulli.


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