How are wages set then?

How would you explain all the fast food chains having to dramatically raise their wages (at least in nominal terms)?

A company that is operating in even a quasi-free market cannot say “you have no skills, the wage for this job is peanuts” in a vacuum. They set a wage and if there are enough people who are voluntarily willing to sign up to do the work, those people are signaling that the wage rate is worth their time. If not enough people who can do the job at sufficient quality appear, the wage rate must increase unit the gap is closed.

I am interested in your alternative to how wages are set.