As von Neumann and Morgenstern pointed out, “very great numbers are often easier to handle than those of medium size.”21 That was exactly the point made by Asimov’s psychohistorians: Even though you can’t track each individual molecule, you can predict the aggregate behavior of vast numbers, precisely what taking the temperature of a gas is all about. You can measure a value related to the average velocity of all the molecules, which reflects the way the individual molecules interact. Why not do the same for people? It worked for Hari Seldon. And it might work for a sufficiently large economy. “When the number of participants becomes really great,” von Neumann and Morgenstern wrote, “some hope emerges that the influence of every particular participant will become negligible.”22
With the basis for utility established at the outset, von Neumann and Morgenstern could proceed simply by taking money to be utility’s measure. The bulk of their book was then devoted to the issue of finding the best strategy to make the most money.
At this point, it’s important to clarify what they meant by the concept of strategy. A strategy in game theory is a very specific course of action, not a general approach to the game. It’s not like tennis, for instance, where your strategy might be “play aggressively” or “play safe shots.” A game theory strategy is a defined set of choices to make for every possible circumstance that might arise. In tennis, your strategy might be to “never rush the net when your opponent serves; serve and volley whenever you are even or ahead in a game; always stay back when behind in a game.” And you’d have other rules for all the other situations.
There’s one additional essential point about strategy in game theory—the distinction between “pure” strategies and “mixed” strategies. In tennis, you might rush the net after every serve (a pure strategy) or you might rush the net after one out of every three serves, staying back at the baseline two times out of three (a mixed strategy). Mixed strategies often turn out to be essential for making game theory work.
In any event, the question isn’t whether there is always a good general strategy, but whether there is always an optimum set of