I use the "first one to PayPal me gets it" line in some of my ads. I usually do that when I'm offering a lot of problem feeders or something. I do this becuase I know that they will go fast, and I want people to know what is going on up front. However, there are other times, when I need to reduce my load of animals, and I price them low to sell fast. Either way, the customer knows that there is the possibility to get an animal for less than market price, but the need for movingfast is obvious.
However, this practice is also beneficial to me as the seller because I let people know that there won't be any "Oh, I really want those snakes, and the check is in the mail" junk going on for me. The first person to email me what I have honestly asked for will get what I have honestly represented. People either trust me, based on my reputation for honesty, or they don't. It's really that simple.
I have had multiple PayPal payments show up before, and I have immediately refunded those that came in second or third. I have no doubt in my mind that if someone were to PayPal me a much larger sum after that first requested sum was entered, that I would politely refund the larger amount (though I would probably try my best to find another animal for that customer!)).
I wonder, if a person were to email saying "I want that animal for X amount of dollars," the seller accepts that offer, the buyer sends the money, and another buyer offers more for the same animal, will that seller be any less tempted than he would have been had he used PayPal in the manner I do? To me, it still boils down to the honesty of the seller. You can either trust him/her or you cannot. People know they can trust me to do what I say I will, and they send me money for animals on PayPal, trying to beat out the others who trust me just as much. I just cannot see that as being a bad thing, or really any different than what would happen if I was just looking to see who emailed me first, or sent me the first money order.