I'd add that just looking at how families or circles of friends operate is also enlightening. The most cynical view is that these interactions are 'debt' based, but practically speaking that often isn't true either. I help my mother not because I calculate the effort she has invested in me or the value she brings me. I just do it because I love her and I don't need to think about how I've come to feel that way (which very well might be based on measurable behavior on her part).
The problem of a free-rider is ever present, and in big cities, that problem is evident and thus you don't get the sort of community effort that you see in a small village.
Beyond Dunbar’s Number, it’s not clear that you can employ mutual-aid theories like tit-for-tat to restrain free-riding and cheating.
What is present in rural areas is a sort of respect and fear of exclusion (I think these two are reciprocal). But it is not impossible to have that on a local level in a large city. Having lived in both London and New York (similar population size, vastly different population density) I've seen this happen. In Manhattan specifically there is little respect for neighborhoods—comparatively—while in London residents care for their boroughs. Some direct actions that might have fostered that are simple things like community gardens/allotments which are very common in the UK.
that's my humble opinion, I'm not an expert in human social behavior.