Reinhard Selten passed away last week. He shared the 1994 Nobel Prize for developing the idea of subgame perfect equilibrium.

As a professor, I am always on the lookout for good examples of subgame perfect equilibrium, because it’s a fairly hard idea to teach. The obituary got me off looking at Wikipedia, and I found an example of a game that is both good and accessible there.

I won’t copy it over here, but the game is a two stepper: one player chooses their strategy, followed by the other. Each has 2 choices, so there are 4 possible outcomes.

The cool thing about the example is that it has 2 Nash equilibria, but only 1 of them is subgame perfect. Further, the explanation sets out the extensive form, but then also shows the outcomes in a matrix (which in my experience is easier for students to use to find Nash equilibria).