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

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?