Ah but it might get spammed. We could add a small fee for each write action. But if someone gets too many of the tokens could they alter the history by rewriting it? we need some kind of consensus mechanism, we could reward participation but make it expensive to lie? Make cooperation the winning move in the game. How do we give the tokens value? maybe some kind of natural scarcity to their issuance, or a fee burning mechanism. As more people use the database the value of the tokens will go up too as they are needed for writing to it, which in turn makes it more expensive to attack and safer storage.

That sounds like it might work.