20-Discussion Questions Solutions

20-Discussion Questions Solutions - Lecture 20: Game Theory...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

20-Discussion Questions Solutions - Lecture 20: Game Theory...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online