For dairy, a smaller company Q started about 15 years ago and is probably helping to keep milk prices down a bit since Tine actually has some competition now, but not nearly enough to bring prices down to what you would find across the border in Sweden, for example.
Unfortunately the grocery store situation doesn't help much either. The largest company - NorgesGruppen - controls almost 40% of the grocery stores. The bulk of the remainder are owned by two others. There is very little price competition, and the selection is still very limited, although it is starting to get a bit better (I've been living here almost 7 years now).
If you live close enough to Sweden, and have your own car (or have friends who go frequently), you can save a ton of money on food and alcohol by heading across the border and doing your shopping there. Unfortunately, it's about 1.5 hour drive from Oslo, so I don't have an opportunity to go very often. It's a funny thing, Norwegian politicians tried to pass going over the border off as a "low class" act, and there's even a derogatory term "harrytur" to describe it, but it's still something that everyone does, regardless of income, simply because the price difference is so great.