The Games Game Theorists Play

Several years ago, I acquired a second-hand paperback copy of Game Theory and Related Approaches to Social Behavior, a 1964 collection of academic papers documenting the penetration of game-theoretical approaches into political science at the apogee of the Cold War. I was, at the time, on the trail of a mysterious think-tank enterprise of the era (known as “Project Michelson”) that had links to the Naval Ordnance Testing Station in the Mojave Desert and also ties to brain scientists working in Washington, DC. The whole thing, I knew, had something to do with modeling tactics for nuclear brinksmanship, but all my leads had come up short—snipped in the archival bud, or frayed in fragmentary bibliographies. As did the thread that had led to my acquisition of the volume in question.

So I fanned through the book in a desultory way, feeling morose. But just as I was about to shelve it (doubtless for good), my eye alighted on the very improbable title of Chapter 24: “‘So long sucker’—a four-person game.”

Hmm. Odd. Flip flip. Less than two full pages of text, mostly consisting of the enumeration of twelve concise rules for playing a chip-based game of strategy. An italicized paragraph offered the following by way of introduction:

This parlor game has little structure and depends almost completely on the bargaining ability and the persuasiveness of the players. In order to win, it is necessary to enter into a series of temporary unenforceable conditions. This, however, is usually not sufficient; at some point it may be to the advantage of a player to renege on his agreement. The four authors still occasionally talk to each other.

Which was sufficiently tantalizing that it led the eye back up to the list of authors: M. Hausner, J. Nash, L. Shapley, and M. Shubik.

No ordinary late-1950s pinochle partners those gentlemen. The restlessly brilliant game-theorist-cum-mathematician Lloyd Shapley—winner of the John von Neumann Theory Prize, breaker of Soviet meteorological code during World War II—has half a dozen theories, lemmas, and solutions that wear his name, and he made fundamental contributions to utility theory over a forty-year career at RAND and UCLA. The articulate and imperious mathematical economist Martin Shubik would become notorious for the invention of one of the truly exquisite perversities of non-cooperative rationality, the “dollar auction,” a seemingly innocuous game that can trap unsuspecting players into spending thousands of dollars to buy a dollar bill (look it up, and be warned; do not play…). And “J. Nash” was none other than John Nash himself, that “Beautiful Mind” of legendary power and fragility, the ghost figure I had known as an undergraduate at Princeton, where he haunted the basement corridors of the mathematics building, muttering to himself about the numbers in his head. The Hollywood version (and the Nobel Prize) would come later. One might almost pity Mel Hausner—himself a no-slouch professor of mathematics—being the fourth at such a table.