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Decisions, Games and Equilibrium Solutions

Published online by Cambridge University Press:  28 February 2022

William Harper
William Harper*
Affiliation:
University of Western Ontario
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Extract

Von Neumann and Morgenstern based their theory of games on the representation of individual preferences for outcomes by utilities generated by preferences for gambles over these outcomes. A utility function (an assignment of numbers to outcomes) represents an agent's preferences just in case the agent's preference relation between any two gambles agrees with the numerical relation between their expected utilities (where these expectations are calculated using the objective probabilities specified in the gambles). This representation constrains the utility assignments up to scale transformations (multiplying each value by the same positive number) and adjustments of the zero point (adding the same positive or negative number to each value). This fixes the ratios of differences between utilities of outcomes.

Von Neumann and Morgenstem proposed qualitative constraints on the agent's preferences among these gambles which are equivalent to the assertion that such a utility representation exists. Here is an equivalent formulation of such rationality postulates.

Type
Part XI. Decision and Game Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 2: Volume Two: Symposia and Invited Papers 1988 , 1988 , pp. 344 - 362
Copyright
Copyright © 1989 by the Philosophy of Science Association

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