Science Magazine - October 6, 2017

54 6 OCTOBER 2017 • VOL 358 ISSUE 6359 sciencemag.org SCIENCE

P H O TO : S K Y N ES H E R / IS TO C KP H OT O

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