Game Changers: Stories of the Revolutionary Minds behind Game Theory

This book isn’t what I expected it to be. I had assumed it would be a survey of the history of game theory, told via biographical accounts of the people involved in its development, much as Ian Stewart’s Significant Figures sketched the historical development of mathematics by means of biographies of 25 people that were instrumental in that history. But instead the book turned out to be a sequence of dramatized vignettes, each illustrating some particular kind of game, introduced to the reader by means of imagined discussions involving people involved in the subject.

And therein lie several problems. For one thing, the author writes in the present tense (“he says”, rather than “he said”), a stylistic device that I, personally, find somewhat irritating. But this is really just a matter of personal preference. A much more troublesome aspect of the book is something that might be called the “E.T. Bell syndrome”.

Bell, of course, was the author of Men of Mathematics, a well-known book of biographical chapters of famous mathematicians. The problem is that in Bell’s book historical accuracy sometimes takes a back seat to entertaining storytelling, to the point where the book cannot really be confidently relied on as a source of factual information.

Thus here. Throughout the book, Taschner puts words into the mouths, and thoughts into the heads, of the people about whom he writes. In some cases, this seems relatively harmless, such as when the author writes that John Maynard Keynes was “positively glowing” and “beside himself with joy when he enters his club”. On other occasions, it can be much more troublesome. Chapter 10, for example, recounts John Nash’s experiences at Princeton. It does so by inventing conversations, presented here as actual quotes, with people like Emil Artin and Albert Tucker. We are told, for example, that after talking with Artin, Nash “realizes that the short interview has come to an end — and that Emil Artin is by no means a fan of his.” It would certainly be interesting to know whether Artin and Nash really did have an acrimonious relationship, but the way in which this information is presented, after the author recounts a conversation that he obviously made up, makes it impossible to know.

A few pages later in the chapter, we are privy to another imaginary conversation, this one between Nash and Tucker, where Nash explains to Tucker the game of “chicken”. This discussion is more pernicious, I think, because it actually involves substantive mathematics. We see Tucker ask Nash a question about the game, and the following ensues:

“It’s all the same — you could just as easily put minus ten,” is Nash’s curt response, but then he suddenly remembers the rules of good behavior, rules that do not come naturally from his inner character, but which he has taught himself, like others might learn vocabulary in a foreign language. “Mr. Tucker, sir, take a look at the other two boxes. In the top right is what the players get if Jim continues driving and Buzz swerves away…”

Later on in this conversation, Nash tells Tucker that Nash attempted to discuss these issues with John von Neumann, and that von Neumann “threw me out of his room.” Here again, it would be interesting to know whether anything of this sort actually happened. It would also be interesting to know whether Nash really did make up the game of “chicken”. From the way in which this information is presented, I simply have no idea.

Perhaps an even more egregious example occurs in chapter 8, which recounts the first meeting between Von Neumann and Oskar Morgenstern. (I assume it’s the first time they’re meeting, because in the course of the conversation Morgenstern tells von Neumann what his first name is.) Morgenstern has posed a question to von Neumann about the best strategy for Sherlock Holmes to avoid Professor Moriarity (basing his facts on the Conan Doyle story The Final Problem). The meeting shows von Neumann explaining to Morgenstern, from scratch, the basics of game theory using two-card poker to illustrate the ideas, and concludes, mere moments later, with Morgenstern suggesting that “We should write a book about this” and von Neumann eagerly agreeing “Good idea — let’s do that!”

The idea of writing a book about game theory with somebody you just met and who doesn’t understand game theory completely seems rather sudden (not to mention presumptious on the part of Morgenstern), but that’s not the worst of this chapter, which ends with the author telling us, of von Neumann, “That there could be [non zero-sum games] is something that he simply couldn’t imagine.” I have a great deal of difficulty, to put it mildly, accepting the notion that John von Neumann, of all people, could not imagine games that were not zero-sum, just as I have difficulty that Albert Tucker would have to be told by a graduate student what the entry in a game matrix means.

Taschner engages in this stylistic technique constantly throughout the book, to the point where it is simply impossible to discern what is fact and what is dramatization. To put it bluntly and informally, this drove me crazy.

I should point out here that I have no intrinsic objection to mixing fact and fiction. In fact, I thoroughly enjoy the Nate Heller series by Max Allan Collins, about a private detective who gets involved over the course of several decades with famous historical events and people, from Al Capone to JFK’s assassination. These mysteries are presented honestly as historical fiction, however, and every one of them ends with a lengthy and well-documented discussion by the author of what is fact and what he made up. Game Changers, by contrast, is advertised as a “lively history of game theory”, and will almost surely not wind up on the fiction shelf of any library that purchases it. But this book is not “history”, at least not as I use the term.

In Taschner’s defense, I should point out that he is honest about what he is doing. He himself points out in the preface that “everything that is described in the book is believable and true for the very reason that I made it all up…” The reason he gives in his preface for engaging in this practice is astounding: he states there that it is a “Sisyphean task to present history as it actually was.” Of course, presenting history “as it actually was” is precisely what a historian does, and if a book doesn’t do that, it should not be marketed as “history”, whether “lively” or otherwise.

For these reasons, I cannot recommend this book. Perhaps not everybody will have the visceral distaste for made-up conversations that I do, and such people might enjoy the anecdotes and popularization of the subject. Laypeople with no prior knowledge of game theory might learn some of the basics of the subject, and might also enjoy the concluding chapter, consisting of problems and solutions. But for people who are interested in learning some of the actual history of the subject, I think something like Poundstone’s Prisoner’s Dilemma is a better bet.

Mark Hunacek (mhunacek@iastate.edu) teaches mathematics at Iowa State University.