Buyer with most money wins?

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I have searched the forums, and it appears I am the only one who has asked this question. Probably not, but I tried all the keywords I could think of, and it didn't show up...and didn't want to have to skim through over 1,700 posts!

Anyhow, I just showed a property this Saturday and one of the potential buyers said they wanted the place and wanted to know if they could put earnest money down to hold it. Since it was the only offer I'd been given in months, I said sure, if they could put $2,000 earnest money in escrow I'd hold off advertising and showing while they ran their application through my RMLO. Well, 96 hours later they finally made it to the bank to deposit the earnest money, but still haven't even filled out the app. I check in with them daily to try and keep on top of it, but I don't want to have to hold their hand all the way to the closing table.

So here's the twist, someone that had seen the property a week prior, just called today and said they wanted the place. I informed him of the situation, but he said he is willing to put down more money, plus he makes better income. Of course, I would still put him through the same screening process with the RMLO to make sure; but before I have him pay the application fee and go through the process I want to make sure I can do this without getting into some sort of trouble. I didn't make any promises or sign anything with the first guy, other than I would hold off advertising and showing, but this guy looked at it a week prior to them. And he is willing to put down $10K more, pay more monthly, and structure a shorter term to payoff quicker (i'm selling with seller financing).

Has anyone encountered this and how did you handle it?