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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 ...
However, Neumann and Morgenstern mentioned that a theory of subjective probability could be provided, and this task was completed by Jimmie Savage in 1954 [7] and Johann Pfanzagl in 1967. [8] Savage extended von Neumann and Morgenstern's axioms of rational preferences to endogenize probability and make it subjective.
Oskar Morgenstern (January 24, 1902 – July 26, 1977) was a German-born economist.In collaboration with mathematician John von Neumann, he founded the mathematical field of game theory as applied to the social sciences and strategic decision-making, as well as making major contributions to decision theory (see von Neumann–Morgenstern utility theorem).
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 ...
Von Neumann-Morgenstern utility theorem; Harsanyi's utilitarian theorem; Arrow's impossibility theorem; Revealed preference theory deals with representing the demand function of an agent by a preference relation, or by a utility function. [7]
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:
In the 18th century, Daniel Bernoulli introduced the concept of "expected utility" in the context of gambling, which was later formalized by John von Neumann and Oskar Morgenstern in the 1940s. Their work on Game Theory and Expected Utility Theory helped establish a rational basis for decision-making under uncertainty.