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Price competition (4 points) There are 100 consumers in the suburb Little Italy all of whom buy either one medium pizza or nothing

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Price competition (4 points) There are 100 consumers in the suburb Little Italy all of whom buy either one medium pizza or nothing. Each consumer has a reservation price of $15. That is, each consumer is willing to pay at most $15 for a medium pizza. There are two pizza stores - A and B - located next to each other. It costs $7 to make a medium pizza. The price of pizza is in whole dollars (e.g., $8, $7, but not $6.99 or $8.50) Let pa and po denote the price charged by stores A and B respectively. For simplicity, assume p; E {1, 2. ... 15) for both i = A, B. If p, < p;, all consumers buy pizza from store i as long as p, < $15. If p, = p = p. and p < 15, then 50 consumers buy from store A while 50 buy from store B.

(2 points) Find out all Nash equilibria in pure strategies. (iii) (2 points) Are all equilibria in (ii) admissible?