There is a hint of a connection to game theory in Adam Smith's Wealth of Nations. For example, he says:
It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.
We can put his general argument into a payoff matrix, like shown below:
There are two Nash Equilibria here: {DS,DS} and {S,S}.
Obviously, if they both specialize, they are both much better off. However, each of them not specializing is also an equilibrium.
Is there any way that Game Theory predicts the emergence of specialization in a population of such players?