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I don't see why consumers wouldn't just pick the stores that have better prices for them. Why would they know/care/need to know what the prices are doing for other people?
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You can't see you mean? Consumers pick things that are reasonably convenient, achievable and known to them. These things are all subject to exploitative tactics by grocery stores.

There's also price-fixing, which famously occurred in Canada recently.

Not to mention cornering a market like Walmart would and removing consumer choice entirely.

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