[doublespanner]

It's because both competitors are making the same calculation where a loss in market share is worth less than the per unit profit increase.

This isn't really a matter of competition, it's that people's willingness to pay (in nominal value) is much higher.

If people's willingness to pay were less, then increasing prices would loose a greater portion of the market.

[mitthrowaway2]

How is the calculation you're describing different than the calculation of optimal pricing for a monopoly?

[doublespanner]

It's similar, but when the price of the product is closer to the willingness to pay, market share becomes important again.

It's also has an impact on what products get made, and investment in r&d. If you fall behind the competition in terms of quality, you loose marketshare.