Lack of competition is impossible. We're biological organisms vying for mating rights and we're never happy unless we've established some kind of pecking order where we've decided who's qualitatively at the top, whose at the bottom, and whose somewhere in the middle.
If we go to a society where our every material need is taken care of none of that will change and as usual we'd have to invent games to create in-groups and out-groups. Life in general would be richer if we used the new-found free time wisely but it could just as easily turn really sour if we can't come to grips with what we are and moderate our heirarchy-making tendencies in a healthy manner.
I think this is also one of the key areas where Marxists really got things terribly wrong - ie. they didn't pay any heed to what Darwin was saying.
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The loneliest part of life: it's not just that no one is on your cloud, few can even see your cloud.