Granted[1], but that doesn't really suggest that we evolved intelligence in order to compete as either individuals as tribes, or address what I'm saying about how intelligence is more useful for cooperation than competition.
[1] I think my wording was confusing, reading my comment I do seem to imply that such competition doesn't exist rather than that I thought it was being overstated, but that was sloppy writing on my part.
Sure, cooperation would be helped by intelligence. However, evolution only occurs under selective pressure, and would cooperation (which reduces pressure) require great intelligence? Cooperation exists widely in the animal kingdom.
The question arises in the framework of an evolutionary "arms race", and what feature of the human environment challenges specifically their intelligence, except other humans?
Their ability to survive in a rapidly changing climate, where they may have to assess whether plants they have limited experience with are edible, or work together to take down bigger game, or generally exercise creativity in the face of novel challenges; additionally, the resources unlocked by intelligence can be their own pressure.
Evolution isn't strictly driven by competition. It isn't reducible to an arms race. If the niche of "intelligent hominid" is a blue ocean, then the evolution can be driven by the vacuum the species is expanding into rather than being pushed by competitive forces. The species does better not because another species does worse, but because they're able to make better use of resources or access resources not previously available.
Competition comes into play more when there is a limiting resource, and the result is generally segmentation, where both species (or presumably hominid communities) adapt in such a way that the resources are divided in a way that meets everyone's needs. When the resource stops being limiting, the competition stops exerting significant pressure.
If evolution was strictly driven by competition, you'd expect instead that species would reliably compete to extinction. But that's actually rare.
Evolution is frequently driven by competition between members of the same species, independent of resources available. Witness the elaborate feathers of many birds of paradise which evolved to secure mating partners, or the antlers of deer which serve during ruts to compete for harems of does.
I feel as if I'm repeating myself but that doesn't address whether or not that's true in this case or address the reasons I've provided for why I don't think so. Afterall I mentioned peacock feathers in one of my first comments, I'm aware of intraspecific competition.
Since we've made two laps around this point I suspect we'll have to agree to disagree.
Cooperation per se doesn't result in pressure to evolve, unless it is cooperation against an outside competitor, see for example herd animals or the care of offspring.
Hence the reasoning above that the human intelligence evolved in competition with something that required increased intelligence to overcome; the only such thing on the planet throughout human evolution is other hominids.
Evidently, this is simply a hypothesis, and doesn't exclude other evolutionary pressures.
