Hidden-Field Coordination Reveals Payoff-Free Quantum Correlation Structure in Decentralized Coordination

Abstract: We study decentralized multi-agent coordination where agents must correlate actions against an unobserved field and cannot communicate. To isolate correlation geometry from payoff optimization, we introduce the Hidden-Field Coordination (HFC) model, which enforces identical information access and no-signaling constraints across strategies. Using information-theoretic diagnostics, we compare classical shared-randomness baselines with an entanglement-mediated strategy based on multipartite W states and a strictly local Spontaneous Leader Election rule. Within the restricted symmetric shared-latent baseline studied here, increasing total correlation is achieved primarily by driving actions toward alignment (copying), which also increases pairwise coincidence (collisions). By contrast, the quantum strategy realizes a collision-suppressing coordination regime: it preserves global dependence while reducing pairwise coincidence below the independent (product) baseline induced by the common marginal distribution. This produces a geometric separation in the joint-action distribution. Classical baselines concentrate probability near the diagonal of action equality, whereas the entanglement-mediated mapping occupies an offset-diagonal region associated with relational roles. Accordingly, the entanglement signature in this setting is not higher correlation magnitude; total-correlation differentials can be negative relative to the classical copying optimum. Instead, it reflects a change in dependence geometry that supports robust anti-coordination.