Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments

We analyze three games using our new solution concept, subgame
perfect equilibrium (SPE). The first game involves players’
trusting that others will not make mistakes. It has three Nash
equilibria but only one is consistent with backward induction. We
show the other two Nash equilibria are not subgame perfect: each
fails to induce Nash in a subgame. The second game involves a
matchmaker sending a couple on a date. There are three Nash
equilibria in the dating subgame. We construct three corresponding
subgame perfect equilibria of the whole game by rolling back each
of the equilibrium payoffs from the subgame. Finally, we analyze a
game in which a firm has to decide whether to invest in a machine
that will reduce its costs of production. We learn that the
strategic effects of this decision–its effect on the choices of
other competing firms–can be large, and if we ignore them we will
make mistakes.