MY COMMENTARY:
Assuming they have the full purchasing power of Delhaize behind them (Food Lion, Hannafords, etc.) taking on Publix might make sense. Not so much with taking on Walmart, if they are in the fray.
At the end of the day, shoppers are not nearly as focused on price as is commonly thought. On a conscious level, price always comes to the fore, whether interviewing shoppers or having a discussion with brands or retailers. This is because, consciously, everyone is trying to at least sound rational. However, shopping is very far from rational, and pricing plays a very small part in most shoppers' regular shopping trips. As long as the store has a value image, other factors will control.
Perceived value is far more important than price, to all but the aggressive bottom-feeder shoppers, that every retailer would be better off losing. This puts a whole different spin on price. The most important role of price is not to tell shoppers what this will cost them, but what it is WORTH! That is the value proposition, and why price alone is an inadequate strategy. But EDLP is CLEARLY superior to Hi-Lo. As I referenced yesterday.