Dear colleagues,
Below is the text of a short letter to the Editor, Notices of Am. Math. Soc.,
April 2008, (posted at http://www.ams.org/notices) concerning game theory
values:
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The assignment of values to objects such as outcomes and coalitions, i.e. the
construction of value functions, is a fundamental concept of game theory. Value
(or utility, or preference) is not a physical property of the objects being
valued, that is, value is a subjective (or psychological, or personal)
property. Therefore, the definition of value requires specifying both what is
being valued and whose values are being measured.
Game theory’s characteristic function assigns values to coalitions so that what
is being valued by this function is clear but von Neumann and Morgenstern do
not specify whose values are being measured in the construction of this
function. Since it is not possible to construct a value (or utility) scale of
an unspecified person or a group of persons, game theory’s characteristic
function is not well-defined. Likewise, all game theory solution concepts that
do not specify whose values are being measured are ill-defined.
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A more expanded paper entitled “On the Mathematical Foundations of Economic
Theory” (13 pages) and a short summary entitled “Game Theory Foundational
Errors — Part I” (2 pages) can be downloaded at
http://www.ScientificMetrics.com/publications.html
You may also be interested in the sections on decision theory and measurement
theory in the paper entitled “Preference Function Modeling (PFM): The
Mathematical Foundations of Decision Theory” which is posted at the same site.
Errors at the mathematical foundations of utility theory, game theory, economic
theory, decision theory, and other social sciences should be brought to the
attention of the community in order to be corrected.
Yours truly,
Jonathan Barzilai
Dalhousie University
Email: [log in to unmask]
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