I thought this was a fascinating observation so I'll try and recast it into the UK situation.
Imagine a mid level supermarket, say, a Waitrose. Imagine then that a cheapy cheapy place opens next door, say an Iceland or a Lidl.
Imagining? Good, now, what happens to the prices in the Waitrose? Do they rise or fall?
Ah, yes, we've our old correct answer in economics again, "it depends".