Tesco have made a bold move recently by actually admitting in their ads that Asda are cheaper than them on a number of products; as they fight a well publicised supermarket price war.
"945 products are cheaper at Asda, but 1213 products are cheaper at Tesco" sort of thing.
Its quite interesting to see how this might play out, because (for example) Asda might come back and say that 'The products Tesco are cheaper on are those you don't buy often' or even 'That's mostly their economy brand stuff which is worse than our economy brand stuff". Etc.
I understand the idea, and in principle I think its a good one. But it's not without risk, and if Asda fight back things could get messy...