The drive is to maximize profits, not keep them from growing.Exactly. That's why both businesses do better by avoiding a price war then they would by continually undercutting the competitors. You really should read up on game theory. Pricing is not as simplistic as you pretend.
I can hear it in the board room, "Let's keep profits from growing... after all, an income tax fanatic kool aid drinker named your nightmare says it's better that way".