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
Price War
Monopolist
Entrant
In
Accommodat
e
-1
-1
Out
1
1
4
0
4
0
• Is (Out, Price War) a reasonable NE?
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.