Expected-Utility Maximization Theorem

Theorem

Let $P$ be a rational decision-maker.

Let $A$ be a set of possible moves available to $P$.

Then there exists a way of assigning values to a payoff function $u: A \to \R$ so that $P$ will always choose the move such that $u$ is a maximum.

Proof

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Historical Note

The idea behind the Expected-Utility Maximization Theorem goes back at least as far as Daniel Bernoulli, who raised the question in his Specimen Theoriae Novae de Mensura Sortis of $1738$ (translated 1954: Exposition of a New Theory on the Measurement of Risk (Econometrica Vol. 22: pp. 23 – 36)).

It was proved by John von Neumann and Oskar Morgenstern in their Theory of Games and Economic Behaviour, 2nd ed. of $1947$.

Sources

• 1991: Roger B. Myerson: Game Theory ... (previous) ... (next): $1.1$ Game Theory, Rationality, and Intelligence