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Game theory gives the players solid recommendations on their optimal strategy and provides an external observer with a prediction of the outcome of the interaction.
In the movie one character suggests that every boy should go it alone disregarding the others, recalling Adam Smith's (1723-1790) famous dictum "in competition, individual ambition serves the common good".
Finally, we discuss why in such coordination problems--unlike in prisoners' dilemmas--simply communicating may be a remedy.
We apply the notion of Nash Equilibrium, first, to some more coordination games; in particular, the Battle of the Sexes.
While "one for the blonde" is Pareto-optimal, the Nash/Crowe configuration is not, since anyone will be better off by switching to the blonde while the rest will not be worse off. However, "one for the blonde" does not suffer from this inconsistency: no one can improve by deviating from his strategy. There are as many possible solutions as guys in your group. Well, here is a solution: watch your group for a second, is George Clooney there? No question about self-evidence in your Clooney case.
So the "best for the group" promised by Nash/Crowe comes from strategic choices that differ from his proposed tactics. Indeed, either the guy going for the blonde or anyone aiming at a brunette would be worse off by changing their strategy unilaterally. This is a Nash equilibrium solution, as proposed by Nash in 1950. So far so good, except for one thing: Clooney could not make it and he's not at the bar today.
The situation at the bar is an example of a game: the boys are the players and the actions they may choose (either "go for the blonde" or "go for a brunette") are called strategies.
This important property is known as Pareto optimality, after the Italian economist Vilfredo Pareto (1848-1923). Schelling, 2005 Nobel Prize laureate in economics, called a focal point.
Economists use Pareto optimality to evaluate overall wellbeing. "No one for the blonde" lacks self-interest consistency, since anyone would be better off by switching to the blonde provided that everybody else goes for a brunette. A focal point is a Nash equilibrium that emerges spontaneously, in a self-evident way.
Furthermore, "one for the blonde" is better for the group than the Nash/Crowe proposal.
"Better" means that no change of strategies can make someone better off without simultaneously making someone else worse off. The solution "Clooney goes for the blonde" is what Thomas C.