dominance and status-driven competition as traditionally masculine
Many women are intensely status-driven (look at their shopping habits, etc.) and dominance is not uncommon, though usually in a "softer" way.
The stereotypical female shopping habits are high-quantity, mid-quality and low price i.e. hunting for discounts and sales. This is not really a status game. A guy is more likely to have status-oriented clothing habits i.e. have only 5 t-shirts but all of them have Armani Jeans written over them in big letters telegraphing the "I am rich, hate me" message :)
I think what you see as dominance amongst women is more often group acceptance / non-acceptance, i.e. popularity vs. marginalization e.g. http://www.urbandictionary.com/define.php?term=teenage...
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