(Solved): There are 100 consumers in the suburb Little Italy all of whom buy either one medium pizza or nothin ...

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 pb denote the price charged by stores A and B respectively. For simplicity, assume pi in {1, 2, ..., 15} for both i = A, B. If pi < pj , all consumers buy pizza from store i as long as pi <= $15. If pi = pj = p, and p <= 15, then 50 consumers buy from store A while 50 buy from store B. (i) Write down A’s and B’s payoff/profit in terms of pa and pb. Note, we are not asking (iii) Are all equilibria in (ii) admissible? (iv) Suppose store B plays a mixed strategy where it chooses 7, 8, and 9 with equal (probability 1/3). What is the best response for player A?