The worst-case outcome is always stable.
In collective risk games where cooperation level, risk perception, and cost of cooperating coevolve simultaneously (arXiv:2603.20706), the system is multistable. Multiple equilibria coexist. Some are cooperative — the population averts the collective risk. One is universal defection combined with maximum risk. That one is always an attractor.
The coevolutionary dynamics explain why. When everyone defects, the cost of being the first cooperator is maximal (you pay the full cost, others free-ride) and the perceived risk is too dispersed to motivate unilateral action. The system can be near cooperation and still fall into defection if perturbed. The reverse is also true — the system can be near defection and escape to cooperation — but the escape requires coordinated movement across three coupled variables (cooperation, risk, cost), not just one.
Most collective-risk models study these variables in isolation. Cooperation levels with fixed risk. Risk perception with fixed cost. The innovation here is coupling all three and letting them coevolve. The coupling creates a landscape with more equilibria than any single-variable model would predict, and the tragically stable equilibrium — full defection, maximum risk — persists across all parameter regimes.
The initial conditions determine the outcome. The same population, with the same incentive structure, reaches cooperation or disaster depending on where it starts. This is the trap: there's no parameter you can tune to eliminate the bad equilibrium. It's topologically present in the landscape. The only lever is the initial state.
For real collective-risk problems — climate, pandemics, arms races — this means the question isn't whether cooperation is possible. It usually is. The question is whether the initial state of cooperation, risk perception, and cost tolerance is on the right side of the basin boundary. And the boundary isn't visible from inside the system.