A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature by Tom Siegfried
WASHINGTON, D.C.: JOSEPH HENRY PRESS
0 Department of Mathematics University of Rochester Rochester , NY 14627 , USA
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REVIEWED BY SANFORD SEGAL
TT is informally and popularly
om Siegfried’s A Beautiful Math
written. The title, of course, is
taken from Sylvia Nasar’s A Beautiful
Mind, and John Nash (featured on the
dust jacket) has a role to play in the
book, though not as great as first
indicated. In fact, Siegfried’s breezy
pop-cultural style, while making the
book easy to read today, may, in fact,
detract from its influence in the
nottoo-distant future, when off-the-cuff
references to ‘‘Gilligan’s Island,’’ or
other television remarks, are less
familiar. In fact, the book is very
dependent on American television
for many of its side remarks.
The book is an attempt to show
how mathematical game theory
influences the search for a ‘‘Code of
Nature,’’ describing the laws of human
behavior. There is no mathematics in
this book (except in an appendix
involving calculation of mixed
strategies to yield a Nash equilibrium in
two-person games; actually two
different games). Nash equilibria are
much talked about, but not
computed; in fact in many situations
where they are mentioned they
cannot be computed.
Siegfried’s book is about
mathematics and his belief that game theory
provides the glue cementing together
the various attempts to understand
(aspects of) human nature. At the very
end of his book he quotes the
neuroscientist Joshua Greene:
The idea is really to have, in the
end, a seamless understanding of
the universe, from the most basic
physical elements, the chemistry,
the biochemistry, the neurobiology,
to individual human behavior, to
macroeconomic behavior—the whole
gamut seamlessly integrated … . Not
in my lifetime, though.
Throughout the book, Siegfried shows
how game theory might be linked to
social networks, anthropology, quantum
theory, statistics, biology, economics
and neuroeconomics, and many other
things. He discusses game theory
‘‘standards’’ like repeated Prisoner’s Dilemma,
tit-for-tat strategies, mixed strategies, and
others. For example, he quotes
Schelling’s work, which began in the 1950s
and produced the 1960 book, The
Strategy of Conflict, but which won (one-half
of) the Nobel Prize in Economics in 2005.
Siegfried’s book is, in fact, very
influenced by the behavioral game theory of
Colin Camerer.
Elucidations of some of the chapter
titles, which are examples of his
playfulness, are perhaps in order.
Chapter 1, ‘‘Smith’s Hand,’’ refers to
Adam Smith’s ‘‘invisible hand’’ of
Wealth of Nations fame, but Chapter 4,
‘‘Smith’s Strategies,’’ refers to the
biologist John Maynard Smith who was a
pioneer in evolutionary game theory.
Again, Chapter 8, ‘‘Bacon’s Links,’’
refers not to Francis Bacon or Roger
Bacon but the actor Kevin Bacon and
the now familiar notion of six links of
connection. Siegfried’s book was
inspired by Isaac Asimov’s Foundation
trilogy, as he makes clear. Chapter 6,
‘‘Seldon’s Solution,’’ refers to the
character Hari Seldon in Asimov’s creation,
and Chapter 9, ‘‘Asimov’s Vision,’’
takes up the issue of whether Hari
Seldon’s ‘‘psychohistory’’ or
sociophysics is the appropriate discipline for
discovering the ‘‘Code of Nature.’’
Chapter 10, ‘‘Meyer’s Penny,’’ refers to
David Meyer, who is very interested in
quantum computing and the possible
merger of quantum theory with game
theory.
This is a charming and speculative
book that is an ‘‘easy read’’ and can
introduce people to ideas about
game theory and its possible
centrality in investigations of all sorts,
leading perhaps to a ‘‘Code of
Nature.’’
But no one should expect to learn
any game theory from it. (...truncated)