4 ideas
The human exploration ship Llanvabon meets an alien ship deep in the Crab Nebula. Neither crew can go home first, because the other might follow and find its home planet, and neither can risk attacking. They resolve the standoff by trading ships: each side strips out its star charts and tracking gear, disables its weapons, and flies home in the other's vessel. Both civilizations gain the other's technology, and neither can be traced.
When two powerful strangers meet and neither can verify the other's intentions, the side that turns away first exposes itself to being followed and later destroyed. Each side therefore sees a preemptive strike as the rational default, even if both would prefer peace. The danger comes from the payoff structure, not from hostility.
Distrust between adversaries ends not through reassurance but through an exchange that makes betrayal physically impossible and cooperation profitable. Each side verifiably disables whatever could be used to harm the other, and both come away with something of equal value. When the deal is symmetric, neither side has to believe the other's promises.
The stalemate is broken by recognizing that the other side faces the same dilemma, runs the same calculations, and fears the same outcomes. Treating the opponent as a mirror of your own logic lets you predict which proposals it can accept. Informal rapport between individual crew members, including swapping jokes, confirms that the two minds are alike enough for that prediction to hold.