Homework 7

Intro Micro--

1. There are two firms, X and Y in an industry. Each may charge a high or low price. The payoff matrix below gives payoffs to each firm. Firm X's profits are listed first in each cell, in millions of dollars.
   1. Does either firm have a dominant strategy? If so what is it? If not,why not? Is there a Nash Equilibrium, if not why not? If the game is only played once what prices do you predict will be charged by the firms and what will each firm's profits be? Answer

   2. If the game is played repeatedly is another outcome or even two possible? Explain. Answer

2. There are two firms, 1 and 2 in an industry. Each may charge a high or low price. The payoff matrix below gives payoffs to each firm. Firm 1's profits are listed first in each cell, in millions of dollars.
   
   
   1. Does either firm have a dominant strategy? If so what is it? If not, why not? Is there a Nash Equilibrium, if not why not? If firms are only allowed to set the price once and for all time (that is the game is only played once, what prices do you predict will be charged by the firms and what will each firm's profits be? Answer

   2. If the game is played repeatedly what outcome do you expect? Answer

3. Consider an industry with two firms. Each firm in the industry can pursue two different strategies, call them X and Y. If Firm 1 chooses strategy X and Firm 2 also chooses strategy X, Firm 1 gets a payoff of 10 and Firm 2 gets a payoff of 4. If both firms choose strategy Y then each gets a payoff of 6. If Firm 1 chooses strategy X while Firm 2 chooses strategy Y then Firm 1 gets a payoff of 4 and Firm 2 gets a payoff of 15. If Firm 1 chooses strategy Y while Firm 2 chooses strategy X then Firm 1 gets a payoff of 4 and Firm 2 gets a payoff of 8.
   1. Construct the payoff matrix for this game. Does either firm have a dominant strategy? Explain your answer. Answer

   2. Define a . Does this game have one or more Nash equilibria? If so identify them, if not, explain why not. If you can, predict how the game will be played by either player in pure strategies if played only once. Would either firm wish to play a mixed strategy? Answer

   3. Suppose the game changes so that if Firm 1 plays strategy X and Firm 2 plays strategy Y Firm 1's payoff becomes 7 rather than 4, everything else stays the same. Does this change your answers about dominant strategies and Nash equilibria? Explain how the game is different and how your predictions about the outcome of the game may be changed. Answer

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