Many applications for rental, can I increase monthly rent ask?

[Tony Hibler]

Hi, we just advertised our rental for $2,750 based on comps and a rental analysis a couple days ago...however we are getting some good applicants.  I feel like we might of undershot the monthly rental amount.  I bet we could get close to $2,950 month based on the responses we are getting.  I have not selected an applicant nor signed any leases.  Wanted to see if I could get a better understanding of the legal ramifications of a move like this (increasing the rent after initial advertisement of the rental and after some applicants have applied).  What is an applicant offers to pay more per month?  ....just looking for more perspectives, also want to be fair to all.