I might need to clarify my point, I don't mean companies like Target or Walmart that have huge numbers of outlets, these companies already compete on $0.01 differences, these companies (in England at least) already do the sort of thing the post describes.
I'm talking about the "normal" stores, the ones that might have 1 or 2 locations in one city, or have 2 or 3 locations across the country, the stores that rely on brand loyalty and don't compete with their competitors on $0.01 difference.
No small business would ever choose to compete on $0.01 price differences; the idea the OP is proposing would cause exactly this.
If you are giving them the inventory management software for free, that is a huge hook for cash strapped small businesses. And once your 'trojan horse' is installed, it's a lot easier to convince a small business owner to 'activate' the product sharing feature to gain an edge over other nearby businesses.
And then as you said, once one business does it, the others follow so that they don't become disadvantaged.
It would seem to me that the key to success is ensuring that your inventory management software is highly intuitive and easy to use for the time-poor business owners.
I'm talking about the "normal" stores, the ones that might have 1 or 2 locations in one city, or have 2 or 3 locations across the country, the stores that rely on brand loyalty and don't compete with their competitors on $0.01 difference.
No small business would ever choose to compete on $0.01 price differences; the idea the OP is proposing would cause exactly this.