Compressive payoff-to-signal transduction can separate the start and sustain thresholds of cooperation

Cooperation is often difficult to start but easier to sustain once established. We ask whether this asymmetry can arise from payoff-to-signal transduction before objective payoffs enter action comparison. In a minimal contribution-sharing game, at a given return factor, cooperation has a net objective disadvantage relative to defection that does not vary with the local cooperative environment. When compressive transduction is applied separately to the two action payoffs, however, the transduced cooperation–defection comparison gap can vary across local environments. Population reweighting aggregates these environment-dependent local gaps into a state-dependent mean comparison signal, whose slope is governed by the environment–gap covariance. In the baseline response map, two branch points satisfy fixed-point self-consistency, tangency, and non-degeneracy, yielding distinct start and sustain thresholds. Analytical derivations, controls, and finite-population tests support this mechanism. The contribution lies in identifying and verifying the conditional cross-level chain linking compressive encoding, population reweighting, and adaptive updating. They also show that whether the deterministic threshold structure is clearly expressed in finite-time trajectories depends on whether the update process reads out the same-environment action gap. These results identify a cross-level mechanism in which payoff-to-signal transduction, population reweighting, and adaptive updating jointly separate the start and sustain thresholds of cooperation.