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Will_Sawin comments on Malice, Stupidity, or Egalité Irréfléchie? - Less Wrong
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So, fearing that A is signalling a desire to leave the group, B discourage A's new behaviour; to counteract this, A seeks out a new peer group, increasing the odds that A does end up leaving the group. So B is engaging in classic self-defeating behaviour ... unless, of course, the peer pressure succeeds.
Unfortunately, B's response to A may well be rational, if B expects other Bs to react the same way, leading A to leave the group unless B can make the peer pressure on A to conform strong enough. The various Bs are in something like the prisoner's dilemma with each other; (if I knew my catalogue of game theory better, I'd be able to say just what they're in).
Well, their problem is not opposing interests. In your model, they seem to have the same interests - they're just at the wrong Nash equilibrium.
Right, it's definitely not PD. And it's not Chicken. As you say, it's one with two Nash equilibria, a good one at both-cooperate and a worse one at both-defect. I just don't remember what it's called and don't know where to find out online.