That's the long story of the struggle for justice for women.
You seemed to say that gender injustice could only be perpetrated by some shadowy caricature "someone." I'm saying there is such a someone: the patriarchy.
On an individual level, perhaps, but how would individual negotiations explain the difference in pay between whole professions (where most of the pay gap is)?
It's not really that individual negotiations explain the larger differences. It's more that the problems with individual negotiations are symptomatic of the deeper gender issues.
I think the people who make such decisions pay everyone as little as possible.