In his bargaining paper, Nash discussed the situation when there is more than one way for the players to achieve a mutual benefit. The problem is to find which way maximizes the benefit (or utility) for both sides—given that both players are rational (and know how to quantify their desires), are equally skilled bargainers, and are equally knowledgeable about each other’s desires.

When bargaining over a possible exchange of resources (in Nash’s example, things like a book, ball, pen, knife, bat, and hat), the two players might assess the values of the objects differently. (To the athletic minded, a bat might seem more valuable than a book, while the more intellectually oriented bargainer might rank the book more valuable than the bat.) Nash showed how to consider such valuations and compute each player’s gain in utility for various exchanges, providing a mathematical map for finding the location of the optimal bargain—the one giving the best deal for both (in terms of maximizing the increase in their respective utilities).⁹

Nash’s bargaining problem paper would in itself have established him as one of game theory’s leading pioneers. But it was another paper, soon to become his doctoral dissertation, that established Nash as the theory’s prophet. It was the paper introducing the “Nash equilibrium,” eventually to become game theory’s most prominent pillar.

The idea of equilibrium is, of course, immensely important to many realms of science. Equilibrium means things are in balance, or stable. And stability turns out to be an essential idea for understanding many natural processes. Biological systems, chemical and physical systems, even social systems all seek stability. So identifying how stability is reached is often the key to predicting the future. If a situation is unstable—as many often are—you can predict the future course of events by figuring out what needs to happen to achieve stability. Understanding stability is a way of knowing where things are going.