It isn't the Realtor accepting the price, it is the owner. At least in my state they are obligated to present every offer. Price is not the only dimension to factor in either. Just off the top of my head: (1) inspection contingency (2) mortgage contingency (or how much to make up for the appraisal) (3) timing for closing (4) lease back option

Can all affect what you would select, not just the price.