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3. Suppose that on Lygon street, there are only two artisan pizzerias, Mario (M) and Luigi (L). They simultaneously decide what price to charge for their pizzas. They can charge $12, $24, and $36. Every day on Lygon street, 60 tourists and 100 residents eat pizza for dinner. Consumers must decide which pizzeria to choose (each person can only go to one pizzeria, must go to at least one, and will consume one pizza). Since tourists do not have any preferences over local pizzerias, 2/3 decide to go to the pizzeria with the lowest price and 1/3 decide to go to the other pizzeria. Residents always go to the pizzeria with the lowest price. If the pizzerias charge the same price, consumers are divided equally between them. (a) (6 marks) Formulate the game strategically: specify who the players are, their actions, and set out the payoff matrix. Is this a game of perfect or imperfect information? (b) (5 marks) Find the pure-strategy NE of the game. If there is more than one pure- strategy Nash equilibrium, briefly discuss which equilibrium the players prefer. (c) (10 marks) Now suppose that Luigi sets its price first, and then Mario, after observing the price of Luigi, decides on the price. Draw the game tree that rep- resents this sequential-move game and find the SPNE. In particular, state the players' SPNE strategies, the SPNE paths, and the SPNE payoffs. (d) (4 marks) Do players benefit from playing sequentially? Briefly explain why