Chayes said. “So there’s a lot of work on game theory models for the growth of the Internet and the World Wide Web.”

In fact, Chayes, Borgs, and collaborators have shown how math that is similar at least in spirit to a game theory approach can explain the emergence of preferential attachment in an evolving network (rather than merely assuming it, as Barabási and Albert did). It’s a matter of minimizing the costs of competing considerations—the cost of making a connection, and the cost of operating it once it has been made. (It’s kind of like buying a car—you can get a cheap one that will cost you more to keep running, or shell out more up front for high performance with low maintenance.) That trade-off can be viewed as a competition between different network structures, and the math that forecasts minimum cost also predicts that something like preferential attachment will describe the network’s evolution.

More explicit uses of game theory have been called on to explain the evolution of other kinds of networks. A popular use of network models, for instance, is in making sense of the mess of chemicals interacting inside living cells. The interplay of thousands of proteins ends up determining how cells behave, which is often a matter of life and death. Game theory can help explain how those biochemical networks evolved into their current complex form.

Biologists would, of course, naturally assume that cellular metabolism should evolve to reach some “optimal” condition for fueling cell activity most efficiently. But what’s most efficient? That depends on the environment, and the environment includes other species evolving toward optimality. “Thus, by evolving towards optimal properties, organisms change their environment, which in turn alters the optimum,” note computational biologist Thomas Pfeiffer and biophysicist Stefan Schuster.¹⁰ And that is just the sort of dynamic for which game theory—particularly evolutionary game theory—is optimal. For example, a key molecule in the network of cellular chemistry is ATP, which provides the energy needed to drive important metabolic processes. ATP is the product of a chain of chemical reactions. To stay alive, a cell needs a