I think the option of a competition with no sponsor should only be followed as a last resource.
It's a good idea, but I'm sure the prizes will be more interesting with a sponsor. But it would be an interesting idea to test as another Side Competition, so 3 competitions total! There could be a competition where users would pay a buy in, that would be used as a prize pool (just like in poker tournaments). If we get a sponsor they could put some added bonus, or a guaranteed prize pool (just like in poker as well).