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# 19. Subgame perfect equilibrium: matchmaking and strategic investments

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Game Theory (ECON 159)

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.

00:00 - Chapter 1. Sub-game Perfect Equilibria: Example
27:22 - Chapter 2. Sub-game Perfect Equilibria: Matchmaking
34:31 - Chapter 3. Matchmaking: SPEs of the Game
49:37 - Chapter 4. Sub-game Perfect Equilibria: Strategic Investments
01:13:15 - Chapter 5. Strategic Investments: Discussion

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

This course was recorded in Fall 2007.