My friend Carol is nice and beautiful. Anyone would bet she has plenty of dates. But it turns out that this is not the case.
The fact is that Carol has dated no-one for ages. And although she is shy by nature, she is also open to adequate proposals and would love to find someone special. But Carol claims that men do not usually approach her. She thinks she frightens them away. Is it just a matter of bad luck? Or is it something else? Maybe Carol has a distorted perception of reality?
Luck is an issue that's naturally addressed in mathematics. If it is a question of luck, mathematics may shed some light on Carol's problem. Let us see.
That’s partly because Nash-influenced game theory isn’t actually a testable scientific theory at all. It is an intellectual tool—a way of organizing our thoughts systematically, applying them in a consistent manner, and ruling out errors. Like Marshallian supply-and-demand analysis or Bayesian statistics, it can be applied to many different problems, and its utility depends on the particular context. But while appealing to the Nash criteria doesn’t necessarily give the correct answer, it often rules out a lot of implausible ones, and it usually helps pin down the logic of the situation.
For these reasons, studying game theory, and learning how to recognize a Nash equilibrium, are highly worthwhile exercises. Once you learn the basics, it is amazing how broadly they can be applied. (Much of the advanced stuff can be safely skipped.) For example, in writing a book about the economics of the financial crisis and trying to figure out why so many people on Wall Street and elsewhere did things that ultimately blew up in their faces, I relied heavily on the Prisoner’s Dilemma, a simple game involving a particular type of Nash equilibrium that shows how certain incentive schemes can promote self-destructive behavior.
My experience wasn’t out of the ordinary. These days, political scientists, evolutionary biologists, and even government regulators are obliged to grasp best-response equilibria and other aspects of game theory. Whenever a government agency is considering a new rule—a set of capital requirements for banks, say, or an environmental regulation—one of the first questions it needs to ask is whether obeying the rules leads to a Nash equilibrium. If it doesn’t, the new policy measure is likely to prove a failure, because those affected will seek a way around it.