[I keep writing the same content over and over, and wanted a canonical place to put it.]
Wages for low-skill labor is not a good market because of differing BATNAs. The BATNA for the marginal employee at an employer is “starve to death”, the BATNA for a marginal employer is “be slightly less efficient”. Minimum wage is designed to work around the BATNA issue, and so there is an optimum level for the minimum wage. Lobbying will tend to keep the minimum wage below that level, and so in general, increasing the minimum wage by a little bit is usually a good idea because it brings up closer to the optimum.
This is a better formalization of the argument typically given as “give people money, they’ll spend it and more jobs are created”. The naive approach to the formalization of this argument ends up being a broken windows fallacy, with the usual counter arguments available regarding opportunity cost. Otherwise, this argument supports raising minimum wage arbitrarily high, and so proves too much — why not raise minimum wage to $1M/hr?
Phrasing it as regulation around BATNA problem shows that there are two ways to solve it: we can keep regulating around the BATNA, with the usual limitations of regulations (e.g., the structure of flat-until-minimum wage will mean that workers who are “worth” minimum wage + $0.5/hr will, because the BATNA is still there, will be making minimum wage). An alternative is to regulate the BATNA away by making sure that people have a different BATNA — in other words, a social safety net. The simplest and easiest social safety net is Basic Guaranteed Income. If we had BGI, we would not need minimum wage, and we would make it easy for businesses to pay employees exactly what they are marginally worth — no more, no less — with no further regulation.
Me, personally? I think instead of regulating the market to work around the BATNA problem, we should fix the goddam BATNA problem (I know, call me crazy). If the BATNA for the marginal employee is “have to subsist on Basic Guaranteed Income”, we won’t need minimum wage laws and all the complexity that comes with them (especially around tipping and enforcement).
If it were up to me, we would be teaching about BATNA is grade-school, because it’s a concept that does a lot to fill the gap of supply-and-demand in understanding how economics works.
Moshe'z 
I don’t see why you think the BATNA of a marginal employee is “starve to death.” There are other potential employers out there who would like to be “a little more efficient.” So if potential employer A says, in effect “I’ll risk being a bit less efficient, because I know that your alternative is starving to death, so you’ll fold and take a lower-than-optimum salary,” the potential employee can say “Hey, look at potential employer B over there! I think I’ll go work for him!”
That is, of course, totally aside from the fact that there is both public charity (various forms of welfare) and private charity to help make the marginal employee’s BATNA something other than “starve to death.”
Simply put, if you really believe that, today, the BATNA for a marginal employee is “starve to death,” you ought to be able to point to some significant number of people who are, today, starving to death.