The simplest example is a rock balanced atop a sharply peaked hill. It’s not a very stable situation, and you can predict the future pretty confidently: That rock is going to roll down the hill, reaching an equilibrium point in the valley. Another common example of equilibrium shows up when you try to dissolve too much sugar in a glass of iced tea. A pile of sugar will settle at the bottom of the glass. When the solution reaches equilibrium, molecules will continue to dissolve out of the pile, but at the same rate as other sugar molecules drop out of the tea and join the pile. The tea is then in a stable situation, maintaining a constant sweetness.
It’s the same principle, just a little more complicated, in a chemical reaction, where stability means achieving a state of “chemical equilibrium,” in which the amounts of the reacting chemicals and their products remain constant. In a typical reaction, two different chemical substances interact to produce a new, third substance. But it’s often not the case that both original substances will entirely disappear, leaving only the new one. At first, amounts of the reacting substances will diminish as the quantity of the product grows. But eventually you may reach a point where the amount of each substance doesn’t change. The reaction continues—but as the first two substances react to make the third, some of the third decomposes to replenish supplies of the first two. In other words, the action continues, but the big picture doesn’t change.
That’s chemical equilibrium, and it is described mathematically by what chemists call the law of mass action. Nash had just this sort of physical equilibrium in mind when he was contemplating stability in game theory. In his dissertation he refers to “the ‘mass-action’ interpretation of equilibrium,” and that such an equilibrium is approached in a game as players “accumulate empirical information” about the payoffs of their strategies.10
When equilibrium is reached in a chemical reaction, the quantities of the chemicals no longer change; when equilibrium is reached in a game, nobody has any incentive to change strategies—so the choice of strategies should remain constant (the game situation is, in other words, stable). All the players should be satis-