An unilateral contract is one the offer makes promise to whoever execute the contract first, such as, I'll give $10 to anyone who get me my lunch before 12:00. Only in this context the deadline matters.
It is not applicable to real estate purchase contract. In your case, offer deadline is an just an advertisement.
I am not sure if there is ethical rule against it, but I am saying you are making a mountain out of a mole hill. The ultimate loyalty the agent lies in getting the best offer. In that way I don't see he's doing anything seriously wrong.
Maybe you should ask for a chance to match the offer. That's the best I can think of.