Game theory is one of the slipperiest topics 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. (Pascal’s wager and the “Monty Hall problem” also make an appearance.)

Historians may question the implied timelessness 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 unfortunate choices, from his non sequitur of a discussion 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 development of game theory. It is perhaps unfair to criticize *Game Changers* on historical, philosophical, 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 Corporation, zero-sum games, and algorithmic notions 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 includes 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.

#### About the author

*The reviewer is at the Department of History, Carnegie Mellon University, Pittsburgh, PA 15213, USA.*