Chapter 13 – Further Practice Questions (With Solutions)
Game Theory and Competitive Strategy
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:
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.
If the manager of each firm is conservative and each follows a maximin
strategy, what will be the outcome?
If Firm 1 chooses Low, its worst payoff, -20, would occur if Firm 2 chooses Low.
If Firm 1 chooses High, its worst payoff, 50, would occur if Firm 2 chooses
High. Therefore, with a conservative maximin strategy, Firm 1 chooses High.
Similarly, if Firm 2 chooses Low, its worst payoff, -30, would occur if Firm 1
chooses Low. If Firm 2 chooses High, its worst payoff, 50, would occur if Firm 1
chooses High. Therefore, with a maximin strategy, Firm 2 chooses High. Thus,
both firms choose High, yielding a payoff of 50 for both.
What is the cooperative outcome?
The cooperative outcome would maximize
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).