observation, experiment, and measurement, and then comparing those numbers with theory. And probability arises not only in making measurements and testing hypotheses, but also in the very description of physical phenomena, particularly in the realm of statistical physics. In the social sciences, of course, probability theory is also indispensable, as Adolphe Quetelet argued almost two centuries ago. So game theory’s intimate relationship with probabilities, I’d wager, is one of the reasons why it finds such widespread applicability in so many different scientific contexts. And no doubt it’s this aspect of game theory that has positioned it so strategically as an agent for merging social and physical statistics into a physics of society—something like Asimov’s psychohistory or a Code of Nature.

So far, attempts to devise a sociophysics for describing society have mostly been based not on game theory, but on statistical mechanics (as was Asimov’s fictional psychohistory). But game theory’s mixed strategy/probabilistic formulas exhibit striking similarities to the probability distributions of statistical physics. In fact, the mixed strategies used by game players to achieve a Nash equilibrium are probability distributions, precisely like the distributions of molecules in a gas that statistical physics quantifies.

This realization prompts a remarkable conclusion—that, in a certain sense, game theory and statistical mechanics are alter egos. That is to say, they can be expressed using the same mathematical language. To be more precise, you’d have to say that certain versions of game theory share math identical to particular formulations of statistical mechanics, but the deep underlying connection remains. It’s just that few people have noticed it.

STATISTICS AND GAMES

If you search the research literature thoroughly, though, you will find several papers from the handful of scientists who have begun to exploit the game theory–statistical physics connection. Among them is David Wolpert, a physicist-mathematician at NASA’s Ames Research Center in California.



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