goals, maximum utilities for Gilligan, the Skipper too, the millionaire, and his wife, the movie star, the Professor and Mary Ann. “This kind of problem is nowhere dealt with in classical mathematics,” von Neumann and Morgenstern noted.
Indeed, Bentham’s notion of the “greatest possible good of the greatest possible number” is mathematically meaningless. It’s like saying you want the most possible food at the least possible cost. Think about it—you can have zero cost (and no food) or all the food in the world, at a very high cost. Which do you want? You certainly can’t calculate an answer to that question. In a Gilligan’s Island economy, it’s not really an issue of wanting the maximum utility for the maximum number, but rather that all the individuals want their own personal possible maximum. In other words, “All maxima are desired at once—by various participants.”19 And in trying to fulfill their desires, every individual’s actions will be influenced by expectations of everyone else’s actions, and vice versa, the old “I think he thinks I think” problem. That makes a social economy, with multiple participants, inherently distinct from the Robinson Crusoe economy. “And it is this problem which the theory of ‘games of strategy’ is mainly devised to meet,” von Neumann and Morgenstern announced.20
Of course, it is easier said than done. It’s one thing to realize that Gilligan’s Island is more complex than Robinson Crusoe’s; it’s something else again to figure out how to do the math. Sure, you can start with something simple, like analyzing the interactions between just two people. Then, once you understand how two people will interact, you can use the same principles to analyze what will happen when a third person enters the game, and then a fourth, and so on. (Eventually, then, you would possess the elusive Code of Nature, once you mastered the math of analyzing the behavior of all the individuals in society as a whole.)
However, you can see how things would rapidly become difficult to keep track of. Each person in the game (or the economy) will make choices based on a wide range of variables. In the Robinson Crusoe economy, his set of variables encompasses all those factors that would affect his quest for maximum utility. But