In case we don't like a logo, we won't use anything and we will pay everyone who participates a share from the 3k.
Everyone who participates? You shouldn't have announced that beforehand, now you are going to get more entries than you normally would, and many of them wouldn't even be original concepts or even created from scratch.
It would have been better if you had only said that, in case, you pick no logo to use, you will only compensate the top 3 participants even if you don't use their logos. This way, those who aren't real graphics designers and have no sense or knowledge of creating logos would stay away from the competition and it would have been easier for you.
Or, you could have some rule or something that could be used to verify that each submission has been created from scratch, maybe like the .ai file or any other if someone is not using Adobe Illustrator but a different software.