So you're standing at the edge of a cliff, chained by the ankle to someone else. You'll be released, and one of you will get a large prize, as soon as the other gives in. How do you persuade the other guy to give in, when the only method at your disposal -- threatening to push him off the cliff -- would doom you both?
Answer: You start dancing, closer and closer to the edge. That way, you don't have to convince him that you would do something totally irrational: plunge him and yourself off the cliff. You just have to convince him that you are prepared to take a higher risk than he is of accidentally falling off the cliff. If you can do that, you win. You have done it by using probability to divide a seemingly indivisible threat. And a smaller threat can be more effective than a bigger one. A threat to drag both of you off the cliff is not credible. A threat to take a 60 percent chance of that same thing might be credible.
This puzzler is dredged up (more or less intact, I hope) from memories of my favorite lecture course in college: "Games and Strategy," taught by Thomas Schelling, who was awarded a Nobel Prize for Economics yesterday. The Nobel honors his role as one of the godfathers of game theory. Schelling's particular gift has been applying the theory to real life. I took the course because it sounded festive, which it wasn't. But under Schelling's spell, the world suddenly looked completely different.
Schelling was never a charismatic figure. Short, gaunt and tweedy, with wire-frame glasses, he talked in a slow, slow monotone, stripping away irrelevant detail and exposing situations ranging from the nuclear standoff of the Cold War to a family's decision about what to have for dinner as stark dramas of warring self-interest. This was game theory.
Classical economic analysis generally assumes that we each take the world as we find it. We can "maximize" our own "utility" (as economists romantically describe the pursuit of happiness) in any circumstances, but the circumstances are a given. Game theory was born to deal with interdependence: situations where what I do depends on what you do, and what you do depends on what I do. That, of course, would cover almost all situations.
For example, what is the best way for two kids to divvy up a candy bar? The answer is easy: I cut and you choose, or vice versa. Why is this the best? Because, like free-market economics generally, it channels self-interest to serve the general interest. The cutter will split the bar as close to evenly as possible, because the chooser will get the benefit of any obvious disparity. You can apply this kind of thinking to a dozen people dividing a large pie, or 300 million people trying to govern themselves.
Economics is the social science that is closest to being a real science. It starts out with a few plausible assumptions about human motives and behavior (basically, that people act rationally in their own self-interest) and derives from them an impressive array of "laws" about the future. Game theory can also be seen as the application of econo-think to non-monetary aspects of life. There's nothing economists like better than to show how someone who seems to be behaving irrationally, or at least is marching to drummers unconnected to rationality one way or another, is actually maximizing utility like, well, mad.
Madness can be wickedly rational. If one of those two folks on the cliff can convince the other that he is just a bit nuts, that makes his threat to drag them both off the cliff much more plausible. Some defenders of Richard Nixon used to claim that the evidence of insanity that bothered a few Americans was actually a purposeful strategy to enhance the deterrent power of our nuclear arsenal.
Another favorite game theory anomaly: Weakness is strength. If you cannot do something, you cannot be forced to do it. A bus driver who cannot open the change box, even at gunpoint, is safer than a bus driver who can.
During the Cold War nuclear standoff, the challenge for both sides was to make a fundamentally irrational threat seem believable. Why would you start a nuclear war when the almost-certain result would be your own national destruction? Why would you even reply to a first strike by the other side with a strike of your own? The classic game theory insight was that your own safety depended on not being too strong. The other side had to be confident that it could survive and retaliate if you went first. Otherwise, in a crisis, it would be sorely tempted to go first.
People associate game theory with nuclear strategy, in part because of the movie "Dr. Strangelove." But game theory's real gift is to make all of life seem like a game. Which it is, isn't it?
Michael Kinsley writes a weekly column for The Post.