ECO290E: Game Theory Lecture 6 Dynamic Games and Backward Induction

Midterm Information 4 or 5 questions; each question may contain a couple of sub-questions. The coverage of the exam is all the lectures (Lec.1-6) except for dynamic games. The exam will take just one hour (at the 6th period on Friday, Feb. 22nd). The maximum points (scores) are 80, not 100. I will explicitly show the maximum points for each question. I plan to have a final exam taking 90 minutes and 120 maximum points; If your performance on the midterm will be not good, you would still have enough chance to recover!!

Review Reporting a Crime  Check the slides for Lecture 5. Cournot Model  Check the handout I gave you in Lecture 4 (You don’t need to care about the iterated elimination argument there, since it is a bit too difficult.)

Dynamic Game Each dynamic game can be expressed by a “game tree.” (it is formally called extensive-form representation) Dynamic games can also be analyzed in strategic form: a strategy in dynamic games is a complete action plan which prescribes how the player will act in each possible contingencies in future.

Entry and Predation There are two firms in the market game: a potential entrant and a monopoly incumbent. First, the entrant decides whether or not to enter this monopoly market. If the potential entrant stays out, then she gets 0 while the monopolist gets a large profit. If the entrant enters the market, then the incumbent must choose whether or not to engage in a price war If he triggers a price war, then both firms suffer. If he accommodates the entrant, then both firms obtain modest profits.

Strategic-Form Analysis Is (Out, Price War) a reasonable NE? Monopolist Entrant Price WarAccommodat e In 1 Out

Game Tree Analysis [to be completed]

Lessons Dynamic games often have multiple Nash equilibria, and some of them do not seem plausible since they rely on non-credible threats. By solving games from the back to the forward, we can erase those implausible equilibria.  Backward Induction This idea will lead us to the refinement of NE, the subgame perfect Nash equilibrium.