Kevin Bryan writes,
Selten’s most renowned contribution came in the idea of perfection. The concept of subgame perfection was first proposed in a German-language journal in 1965 (making it one of the rare modern economic classics inaccessible to English speakers in the original, alongside Maurice Allais’ 1953 French-language paper in Econometrica which introduces the Allais paradox).and
In the 1965 paper, on demand inertia (paper is gated), Selten wrote a small game theoretic model to accompany the experiment, but realized there were many equilibria. The term “subgame perfect” was not introduced until 1974, also by Selten, but the idea itself is clear in the ’65 paper. He proposed that attention should focus on equilibria where, after every action, each player continues to act rationally from that point forward; that is, he proposed that in every “subgame”, or every game that could conceivably occur after some actions have been taken, equilibrium actions must remain an equilibrium. Consider predatory pricing: a firm considers lowering price below cost today to deter entry. It is a Nash equilibrium for entrants to believe the price would continue to stay low should they enter, and hence to not enter. But it is not subgame perfect: the entrant should reason that after entering, it is not worthwhile for the incumbent to continue to lose money once the entry has already occurred.And this idea started a whole industry of finding other ways to refine Nash Equilibria.