Incentive Alignment Reshapes Coordination Over Unreliable Communication

When communication is unreliable, agents with the same objective may need different participation rules. We study Bayesian coordination games in which utilities interpolate between private and group-average payoffs. For full-quorum relay lines with heterogeneous links and an informed root that vetoes unsafe operation, we characterize all coordinating observation-monotone pure equilibria: each consists of a message-responsive prefix and an unconditionally acting suffix, determined by three posterior-odds inequalities. Permuting the same link reliabilities can change the equilibrium assignment while preserving end-to-end reliability, so no scalar summary of the channel determines the local policies. Under a uniform veto condition, equilibrium existence and the best certified welfare are monotone in alignment, although a canonical equilibrium selection need not be. The characterization yields an exact compiler that separates equilibrium certification, welfare-based selection, and local execution. Experiments with open-weight language models distinguish the formal certificate used for audit from the representation given to the executor. On fresh relay games, executing the full audit certificate directly loses welfare relative to not coordinating at all, whereas the same certificate compiled into a local decision-table execution card is executed almost exactly and recovers the welfare of the selected policy; violations of the declared fallback remain when the certificate's assumptions fail. The results connect an exact coordination structure to a local execution interface while separating policy fidelity from validity enforcement.