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The theorem forms the foundation of expected utility theory. In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function, where such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize ...
The expected utility-maximizing individual makes decisions rationally based on the theory's axioms. The von Neumann–Morgenstern formulation is important in the application of set theory to economics because it was developed shortly after the Hicks–Allen "ordinal revolution" of the 1930s, and it revived the idea of cardinal utility in ...
The first important use of the expected utility theory was that of John von Neumann and Oskar Morgenstern, who used the assumption of expected utility maximization in their formulation of game theory. In finding the probability-weighted average of the utility from each possible outcome:
Subsequent developments of thermodynamics even fixed the absolute zero so that the transformation system in thermodynamics consists only of the multiplication by constants. According to Von Neumann and Morgenstern (1944, p. 23), "For utility the situation seems to be of a similar nature [to temperature]".
The most famous example of a utility representation theorem is the Von Neumann–Morgenstern utility theorem, which shows that any rational agent has a utility function that measures their preferences over lotteries.
Given its motivations and approach, generalized expected utility theory may properly be regarded as a subfield of behavioral economics, but it is more frequently located within mainstream economic theory. The expected utility model developed by John von Neumann and Oskar Morgenstern dominated decision theory from its formulation in 1944 until ...
In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be but one has knowledge about the distribution of the uncertainty, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility (a probability ...
Let u(w, x) be an individual's utility function, where w is the person's wealth and x is a dummy variable that takes the value 1 in the presence of an undesired feature and takes the value 0 in the absence of that feature. The utility function is assumed to be increasing in wealth and decreasing in x. Also, define w 0 as the person's initial ...