It's harder to design systems that avoid competitive behavior, but I don't think it's impossible. And of course competition is not all bad, it's a good tool when used carefully. But it's way too much when most of our systems are based on it.
Any sort of scheme to try allocate the funding leads to competition for said funding!
In other words, in order to remove all competition in the system, you need unlimited funding. Even randomly allocating funding is insufficient, as it simply means you're competing on luck (for example, by trying to acquire more slots in the lottery).
> harder to avoid competitive behavior, but I don't think it's impossible.
Which i think is not true - it is in fact, impossible, unless you add in the condition that there's unlimited 'resources' (after all, there's competition for resources while it is limited).
all systems are competitive, if the system involves humans - after all, even in a constrained environment like academia, where research is cooperative, the competition for recognition is still strong. This includes the order of the authorship presented in the paper.
What you're asking for, regarding cooperation to achieve common goals, is altruism. This does not exist in human nature.