First Attack, Final Offensive: The Dark Forest on an Open Roster

Abstract

The Dark Forest argument holds that a civilization that detects another should strike it at once. Existing formal models make the detected civilization the object of the strike and play it on a roster the attacker knows to be complete. This paper changes both choices. The object of hostility is remaining uncontrolled capacity to retaliate or to warn someone who can, and the roster is open: no attacker ever knows it has met everyone. A first strike is then rational only if the timing benefit of what it removes now rather than later is at least the disclosure loss from every survivor that learns of it. A survivor that can bring about the attacker's destruction enters that loss as a lump, not a per-unit rate, and the actors the attacker has never found may be such a survivor, one that no strike removes. Their capacity cannot be estimated, but what they can do is capped at the attacker's destruction, so the test against them asks one answerable question: a first strike is rational only if the attacker accepts that the strike may be its last attack. The Dark Forest premises, read as hypotheses, fix what a general attacker cannot estimate: hidden hunters exist, a hunter that verifies a hostile acts against it with probability at least $q$, and a hider is rarely found, so a believer's first strike is rational only if what it removes is worth a $q$-share of its survival, the whole of it as $q$ approaches one. With survival as the payoff, the profile in which every hunter strikes what it finds is not a Nash equilibrium whenever a strike is more visible to unfound hunters than a hider is findable, while the profile in which every hunter hides is. That visibility comparison is the decisive physical question; an attacker that treats its strike as unseen has assumed the roster closed.