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 Lectur

e 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 War Accommodate

In -1

-1

1

1

Out 4

0

4

0

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.