Lecture 20: Game Theory (I)
Suggested questions and exercises (Pindyck and Rubinfeld, Ch.13).
Exercises: 4, 5, 6, 7
EXERCISES
4.
Two firms are in the chocolate market.
Each can choose to go for the high end of
the market (high quality) or the low end (low quality).
Resulting profits are given
by the following payoff matrix:
Firm 2
Low
High
Low
20, 30
900, 600
Firm 1
High
100, 800
50, 50
a.
What outcomes, if any, are Nash equilibria?
A Nash equilibrium exists when neither party has an incentive to alter its
strategy, taking the other’s strategy as given.
If Firm 2 chooses Low and Firm
1 chooses High, neither will have an incentive to change (100 > 20 for Firm 1
and 800 > 50 for Firm 2).
If Firm 2 chooses High and Firm 1 chooses Low,
neither will have an incentive to change (900 > 50 for Firm 1 and 600 > 30 for
Firm 2).
Both outcomes are Nash equilibria.
Both firms choosing low is not a
Nash equilibrium because, for example, if Firm 1 chooses low then firm 2 is
better off by switching to high since 600 is greater than 30.
b.
What is the cooperative outcome?
The cooperative outcome would maximize
joint
payoffs.
This would occur if
Firm 1 goes for the low end of the market and Firm 2 goes for the high end of
the market.
The joint payoff is 1,500 (Firm 1 gets 900 and Firm 2 gets 600).
c.
Which firm benefits most from the cooperative outcome?
How much would
that firm need to offer the other to persuade it to collude?
Firm 1 benefits most from cooperation.
The difference between its best payoff
under cooperation and the next best payoff is 900  100 = 800.
To persuade
Firm 2 to choose Firm 1’s best opti
on, Firm 1 must offer at least the difference
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 Fall '10
 Tontz
 Microeconomics, Game Theory, japan, Firm

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