While it is possible both would go for low-skill lawyers, in the real world such a low-low outcome is highly unlikely.
The Paradox of Lawyer Skill and Luck
Ken Grady

This is a really interesting thought experiment. What strikes me is that, unlike the classic “prisoner’s dilemma” of game theory, the two sides to a litigation can signal intent. It is possible for a client to engage a “low skill” lawyer first, see how the other side responds, and then evaluate whether to engage “high skill” counsel. (That could happen, for example, by a client asking local counsel to make the first appearance alone.)

Of course, that presumes a level of trust unlikely to exist in a litigation context. If each side perceives an economic benefit to hiring “high skill” counsel, they might engage such a firm to work behind the scenes and appear only late in the case (if at all), hoping to preserve a “high-low” matchup. And if both sides see an economic reason to do that…