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 Section1 Consider the following game where x > 0 Firm 2 High price 140,140 90 + , 90- Low Price 20,160 50,50 High Price Firm 1 Low price | 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 HS 0. 0 Beta 20, 10 Sony 4. 5. 6. 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? 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 equilbrium of this game