54 6 OCTOBER 2017 • VOL 358 ISSUE 6359 sciencemag.org SCIENCE
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Game theory is one of the slipperiest opics in the history of mathematics. Looked at one way, the field is quite narrow. Beginners usually think of it as based around the problem of the “prisoner’s dilemma,” while more
seasoned readers might point to the research inspired by John von Neumann and
Oskar Morgenstern’s 1944 Theory of Games
and Economic Behavior. Broaden the perspective a little, however, and almost everything that can be modeled mathematically
might be considered a game, from Blaise
Pascal’s 17th-century wager that God exists
to a contestant choosing between doors on
Monty Hall’s Let’s Make a Deal.
Rudolph Taschner’s approach in Game
Changers is firmly in this second camp. Despite the title chosen for this English translation of the 2015 Die Mathematik Des Daseins,
the book contains surprisingly little about
the development of the mathematics behind
general-sum and combinatorial games, or
voting schemes and auctions. Instead, it is
loosely structured into a series of vignettes
about game playing, many involving familiar
mathematical puzzles, from the gambler’s
fallacy to the St. Petersburg paradox. (Pas-
Blending fact and fiction, a mathematics professor aims
to breathe new life into the history of game theory
The reviewer is at the Department of History, Carnegie Mellon
University, Pittsburgh, PA 15213, USA. Email: cjp1@cmu.edu
cal’s wager and the “Monty Hall problem”
also make an appearance.)
Historians may question the implied time-
lessness and universality of games, as well
as Taschner’s suggestion that von Neumann
and Morgenstern’s book is best understood as
just another example of game playing rather
than as a foundational text. Philosophically
minded readers will also lament that he
never clearly defines either “play” or “game.”
Taschner certainly makes some unfortu-
nate choices, from his non sequitur of a dis-
cussion of Peter Shaffer’s play Amadeus to his
decision to exclude any substantive analysis
of the role geopolitics, particularly of World
War II and the Cold War, played in the devel-
opment of game theory. It is perhaps unfair
to criticize Game Changers on historical, phil-
osophical, or even mathematical grounds,
however, because Taschner aims only to pre-
sent a collection of fictional “scenes.”
Those familiar with the usual story of
game theory’s creation—the RAND Corpora-
tion, zero-sum games, and algorithmic no-
tions of rationality—won’t learn much new in
Game Changers. Both William Poundstone’s
popular account in Prisoner’s Dilemma and
Paul Erickson’s historical treatment in The
World the Game Theorists Made remain far
more valuable.
That’s not to say that those curious about
the history of game theory will not find
anything of interest. Taschner’s book shifts
the origins of formal game theory from the
United States to Austria, helpfully revealing
the training and mentorship that facilitated
later developments in the field. He also in-
cludes a brief discussion of game theory in
the 21st century.
For math novices, the dialogue in each
“scene” serves as a thin disguise for an introductory lecture on various topics, from
defining a curve mathematically to weighing
strategies in the game of “chicken.” Taschner
uses the chapters to instruct readers how to
approach classic problems, and he includes
practice questions and solutions at the end
of the book to reinforce the basic concepts.
Moreover, it is useful to think about the
broader meaning of a game, and although
Taschner doesn’t gesture explicitly in this direction, one might think of his contribution
as pushing the origins of game theory out
of the Cold War and into a broader history
of decision theory. Herbert Simon’s review
of von Neumann and Morgenstern’s book
(tellingly published in the American Journal of Sociology) situated game theory as a
social scientific contribution to understanding rational behavior rather than as a subset of probability theory. (I work at Simon’s
longtime institution, Carnegie Mellon, and
here a department of “Social and Decision
Sciences” reminds us that the mathematics
of games fits naturally within the realm of
behavioral economics and the psychology of
risk perception.)
Taschner admits that an account based
on invented conversations and dramatized
interactions cannot be historically accurate.
Indeed, some assertions—that von Neumann
“couldn’t imagine” non–zero-sum games, for
example—are downright misleading. It is a
shame that he dismisses the past with the
gloss that it is an overly “Sisyphean task” to
“present history as it actually was.” The topic
is engaging precisely because it involves real
people who struggled with complex problems
and who relied on mathematics for help.
The mathematical concepts that underlie game theory have become hugely consequential in a world the protagonists couldn’t
possibly have imagined—one filled with
mountains of data, wristwatch-sized computers, and decision-making algorithms. Sometimes the truth is decidedly stranger, and
definitely more interesting, than fiction. j
10.1126/science.aao4385
Taschner hints that he may have reached deeper truths about game theory, precisely because he “made it all up.”
Game Changers
Stories of the Revolutionary
Minds Behind Game Theory
Rudolf Taschner
Prometheus Books, 2017.
237 pp.
MATHEMATICS
Fun and games
By Christopher J. Phillips
INSIGHTS