Assume that with probability q, the consumer is a patient person. So he will visit both sellers and compare the two prices. With probability 1 − q, the consumer is impatient and will randomly visit one -1- ECON101 Winter, 2016 of the two sellers with equal probability. As long as the price of the store is lower than v, he will buy it even if the other seller’s price might be lower. Also, we assume that the sellers know the value of q and choose prices before consumer visits.

(a) If q = 1, i.e. the consumer is patient for sure, what’s Nash Equilibrium PA, PB? If q = 0, i.e. the consumer is impatient for sure, what’s the Nash Equilibrium PA, PB?

(b) For any value 0 < q < 1, what’s Nash Equilibrium prices PA, PB? Hints: • Check whether pure strategy NE exists or not. • If not, how about mixed NE?