After Cooperation Is Learned: Gradient Routing and Optimizer-Dependent Maintenance in Multi-Agent Reinforcement Learning

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Cooperative MARL is commonly evaluated through cooperation discovery from random initialization, leaving open whether continued optimization can destabilize learned cooperation. Actor-critic comparisons can also conflate critic presence with value gradients entering shared actor representations. We study cooperation maintenance, defined as the survival of a behaviorally verified cooperative policy under continued training. We formulate maintenance as a right-censored event-time problem and compare matched warm starts: X0 allows value loss gradients to update shared actor features, X1 retains the critic while blocking those gradients, and X5 removes the learned critic as a critic-free reference. This isolates direct value-gradient access while controlling initialization, critic computation, and evaluation. Positive reward scaling preserves strategic preferences and equilibria while perturbing learning dynamics. Gradient audits confirm the intended routing pathways, and frozen-policy torso perturbations probe whether route-induced updates align with local cooperation boundaries. In confirmatory MinEx and CleanUp-lite experiments, higher scales selectively increase maintenance sensitivity in X0; X1 remains near the censoring ceiling, and X5 has no confirmed events in the tested settings. In CleanUp-lite, route-by-scale displacement is associated with reduced local cooperation margins; MinEx shows a weaker, optimizer-dependent effect. These results identify a conditional, scale-sensitive maintenance risk associated with direct value-gradient routing rather than a universal failure of critics.