Game theory more or less dictates that such a situation would be unstable. Even the slightest tendency to cheat would have massive rewards for the individual so such behavior would evolve again quickly.
Depends on what is meant by "rewards". In such a world, the concept would have a very different meaning. After all, what's the point of cheating to get a billion dollars if you and everyone else already has a billion dollars?
We have become so committed to our selfish actions that we are reluctant to admit the fundamental pointlessness of them...
