@Brad E. I wouldn't pay 11k over the appraisal value. Of course, sometimes appraisers aren't very good. When buying a property, especially using a loan, the agent should be there during the appraisal to make sure they know the comps in the area and to get you an appraisal that is right.
If you're getting a loan, the bank probably won't let you purchase it for anything over the appraisal. If you're paying cash, do the numbers still work even for 11k over? Maybe they do and it makes sense to move forward because the numbers work. That may be why the others are moving forward with their deals. They might not be running the numbers correct though so I wouldn't just assume it's worth it because they're buying it for a higher price.
Also, you're using an agent, he/she should be getting you the market value and suggesting what to offer. You're paying them for their service, I would let them do that and you analyze the rental numbers part of it. I trust my agent to run the comps and analyze what a property's market value is. I only trust myself when running the rental numbers.
Good luck!