I can't comment about then innovation aspect that much, but Bengal (particularly East Bengal, present day Bangladesh) absolutely had/has a huge culture of sharing. People would share meals and socialize even when they themselves were barely able feed themselves (and this was mostly reciprocated). This may be more of generosity than strictly cooperation, but I would say they're quite related.

Source: The stories I've heard from my grandparents (I'm Bengali)

For example, in many non-individualistic societies, if one is to come upon some extra wealth, in manner of for example successful hunt, bountiful harvests, or good government job, one is duty-bound to share that extra wealth with others in their clan or tribe. This disincentives trying hard and increasing productivity: if, through increased labor and investment in fertilizer you can double your yield, but then only get a small fraction of that gain for yourself, why bother trying in the first place? In fact, it might be better investment to obtain higher status in your clan or tribe, so that others will be bound to share more of their wealth with you.