The two firms in question are Nokia and Sony Ericsson. Both companies have cut pricing on their mid- to high-tier handsets by about 10% on average. This means phones such as the $750 Nokia N96 now cost $675. What do you think, is that going to do it for you? Is a $675 cheap enough to convince you to buy? The prices of Nokia's high-end devices sink slowly over time with out without competitive price drops. According to Reuters, though, Nokia has lots of unsold phones hanging about.
The sweet spot for smartphones is in the $150 to $300 range (after subsidies). Consumers are getting powerful phones for decent prices at the moment. Many of the most popular phones cost $100 or less.
Vendors such as Apple, RIM, and HTC would need to feel threatened significantly by a dramatic slow-down in sales or price reductions by competitors for a full-scale price war to break out. Since Nokia and Sony Ericsson are based in Europe, and the phone models with the (stingy) 10% price drops are sold mostly in those markets, I don't see a real price war breaking out in the U.S. market anytime soon.