So game-theoretically: if I know the price for an item is the same everywhere, I'll buy it at the place where I see it first (one of the big values of brick and mortar stores).

If I know I can go online and it'll be some % cheaper, I'll wait and order it online, defer my gratification for a few days, and end up with a cheaper product.

Not sure about Poland, but most B&M brick and mortar stores in the US are distributors/resellers of the brand, they buy for $4 and sell for $10, and their rent/labor/etc costs $3 and they profit $3. Another distributor let's say is an e-commerce website, they can setup a warehouse in a rural area with cheap labor so it costs them $1 and they profit $5... so they can afford to discount it to $7 and make $2... which the B&M store can't do because they won't profit at all.