LLM-based agents increasingly coordinate decisions in multi-agent systems, often attaching natural-language reasoning to actions. However, reasoning is neither free nor automatically reliable: it incurs computational cost and, without verification, may degenerate into persuasive cheap talk. We introduce Explanatory Equilibrium as a design principle for explanation-aware multi-agent systems and study a regime in which agents exchange structured reasoning artifacts-auditable claims paired with concise text-while receivers apply bounded verification through probabilistic audits under explicit resource constraints. We contribute (i) a minimal mechanism-level exchange-audit model linking audit intensity, misreporting incentives, and reasoning costs, and (ii) empirical evidence from a finance-inspired LLM setting involving a Trader and a Risk Manager. In ambiguous, borderline proposals, auditable artifacts prevent the cost of silence driven by conservative validation under asymmetric information: without structured claims, approval and welfare collapse. By contrast, structured reasoning unlocks coordination while maintaining consistently low bad-approval rates across audit intensities, audit budgets, and incentive regimes. Our results suggest that scalable, safety-preserving coordination in LLM-based multi-agent systems depends not only on audit strength, but more fundamentally on disciplined externalization of reasoning into partially verifiable artifacts.

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