Problem Set 5 (Game Theory) Please provide your answers on a separate sheet. Write as neatly as possible, show all your work and clearly note your final answer Section 1 Consider the following game where x >0: Firm 2 High price Low Price High Price 140,140 20, 160 Firm 1 Low price 90 +x,90-x 50, 50 1. 2. For what values of x do both firms have a dominant strategy? What is the Nash equilibrium for these cases? For what values of x does only one firm have a dominant strategy? What is the Nash equilibrium for these cases? Are there any values of x such that neither firm has the dominant strategy? Ignoring mixed strategies, is there a Nash Equilibrium in such cases? 3. Section 2 Consider the following game between Sony, a manufacturer of video cassettes players, and Columbia Pictures, a movie studio. Each firm must decide whether to use the VHS or Beta format- Sony to make video players, Columbia to release its movies for rental or purchase. Columbia Pictures Beta VHS Beta 20,10 0,0 HS 0,0 Sony 10, 20 Restrict attention to pure strategies. Does either firm have a dominant strategy? What are the pure strategy Nash equilibria of the game. Is there a mixed strategy Nash equilibrium of this game? If so what is it? 4. 5. 6. Restrict attention to pure strategies, but now focus on a sequential move game in which Sony chooses its strategy first 7. Draw the tree that represents this new game and determine the Sub-Game Perfect Nash equilibrium of this game