Game Theory: Mercedes and BMW release a new car model. Each can release either a "sport" model or a "luxury" model. The companies prefer product heterogeneity in their releases: in other words, both companies receive a payoff of zero if they release the same type. If the types are different, the company with the "luxury" ("sport") model receives a payoff of 100 (50). a. (1 pt) Suppose Mercedes and BMW make their model choice simultaneously. Draw the payoff matrix. b. (3 pts) Find the Nash Equilibria in pure and mixed strategies. c. (3 pts) Suppose Mercedes has a first-mover advantage. Draw the extensive form of this game, and solve for the Nash Equilibrium.