I'm probably going to get hate on by the females here, but just presenting the facts for my fellow males here.
40-50% of American marriages end in divorce. 66% to 90% of those divorces are initiated by females. If you're a college-educated couple, 90% of the time it's initiated by the woman. When you add that mothers will gain custody 68-88% of the time, those are horrible odds for us guys.
By no means am I discouraging marriage for guys. I just think it's worth looking at more critically and understanding that it's a choice, not an obligation. Look at your assets and hers, your own liabilities and hers, etc.
From the cite you provided, I read the more recent article (I didn't think one from 1975 or 1988 to be as relevant today).
http://www.unc.edu/courses/2010fall/econ/586/001/Readings/Brinig.pdfYou may find it interesting to know that the paper does conclude one reason people file when they are being exploited in the marriage. Another is to gain custody. Re the horrible odds you describe, note that: "Even by the most conservative accounts, the average divorced woman's standard of living declines from the one she enjoyed during marriage, and it declines relatively more than does the average husband's."
When you say women gain custody 68-88% of the time, are you talking physical custody? I saw support for your other comment, but not this point in the wiki article you discussed. Today it is extraordinarily rare for parents not to share joint legal custody. Arrangements for physical custody vary, but my understanding is that most states follow "Best interests of the child" standard, which is then interpreted to be in the best interests of the child that they have time with both parents. Thus, most parents do share joint physical custody too, although one parent may have more time overall than the other. It's also a chicken and egg problem - one reason women tend to get more time than men when sharing physical custody, is that they are more often to already be working part-time (or staying at home) to take care of kids than dads.
I've worked pro bono for a family law clinic and served pro bono as "Lawyer for a Day" in the family court in another state, and I observed that many men do not seek custody. (Note, many more of course do, but it is worth noting more men choose not to than women, thus skewing your above figures. Ancedotally, I can say this is often lower income families where the father has children by multiple women.) Sadly, in other cases the men seek custody solely to avoid paying child support. One thing we would advise a parent is to consider this likelihood (and how much it mattered to them), in deciding whether to file just for custody or for custody & support.
I can only speak ancedotally on this, but at least in the cases of divorces I've known - when it was mutually agreed to divorce, the men "let" the woman file as some type of courtesy. I don't exactly understand it, I'm just reporting what they told me.