My point exactly!
If you think you are going up against me at any time, you won't sell me your best chain at any price!
And conversely, I wouldn't trust you to sell me a chain. I know I'd be getting barbed wire.
By sharing the purse, both filer and competitor will put their best effort forward.
Then at some point, the sawyer will want to cut the sharpener out of the profits, and will copy his work, then claiming to be the best "all around".
Meanwhile, the sharpener will be working on the next prospect. Very few people can be the best at all aspects of anything, so in the end, both will continue to be successful.