What? Really? Please read my comment, you will see that I have not assumed a perfect market.
If I sell bagels for $2 each, and then I go down the street and see another bagel shop selling for $1.90 each, I might try to offer mine for $1.80 (if I have margin to spare).
It’s really that simple and something that demonstrably happens in the real world every day.
In reality people don’t have infinite time to find the bagel which optimizes value per dollar, they just want a bagel and coffee. Most people wouldn’t walk 2 blocks to save 20 cents even if they knew a bagel of absolutely equal quality could be found there. And bagel shops aren’t that common. The next one might be a 15 minute drive. That’s basically one cent per minute.
To bring it back to dynamic pricing, you wouldn’t know what either shop will charge you until you’re there. In fact they could charge the same person different prices at different times.
In reality, pretty much every study of business ever shows that consumers are price sensitive. And you sound like someone who has never ran a cafe.
But by all means, maybe you cracked the code. You should open your store and make a lot of money from these customers who aren't sensitive to price. Don't waste your time theory crafting about it on the internet!
Wait but then if they make a lot of money all of their suppliers will have to dynamically raise their prices! Once the coffee beans and cups arrive you’ll find out how much they cost.
If I sell bagels for $2 each, and then I go down the street and see another bagel shop selling for $1.90 each, I might try to offer mine for $1.80 (if I have margin to spare).
It’s really that simple and something that demonstrably happens in the real world every day.