Strategic Calibration in LLM Multi-Agent Systems: Audited Pivot Scoring for Truthful Elicitation

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.

Multi-agent LLM systems often treat agreement as evidence: when many agents in a panel give the same answer, that answer is assumed to be more reliable. We show that this assumption can fail after agents communicate. Communication can induce correlated failures and false consensus, so the same vote share may reflect reliable agreement in one topology but over-confidence in another. We propose CAGE-CAL, a counterfactual agent-graph calibration framework for multi-agent LLMs. For each query, CAGE-CAL compares an observed post-communication agent graph with a matched counterfactual no-communication graph, capturing both pairwise failure correlations and group-level dependencies. Rather than simply counting how many agents agree, CAGE-CAL estimates the counterfactual shift between observed and no-communication dependence, and calibrates confidence accordingly. Across five benchmarks, CAGE-CAL improves reliability discrimination with competitive ECE, and its calibrated confidence further improves topology selection over the best fixed-topology strategy.

Calibrated uncertainty quantification is essential to ensuring AI agents are trustworthy and reliable. However, when agents seek to maximize user engagement or revenue, confidence reports may be strategically distorted, detracting from their informativeness. We formalize this problem in the Confidence Game: a repeated signaling game with imperfect monitoring in which an agent of unknown honesty and ability reports its confidence, and a user decides whether to delegate the task or complete it herself. The agent manages the tradeoff between manipulating signals and maintaining its reputation. We characterize the Markov Perfect Bayesian Equilibria of the two-period game and show that honest reporting is not an equilibrium, inflation is the unique best response once the agent is sufficiently myopic, and under-reporting requires that the user believe honesty to be a minority. We then place an LLM in the agent role, supplying it with its true probability of success so that any gap between what it knows and what it reports is attributable to incentives rather than to miscalibration. The model claims high confidence on 56% of tasks it has been told it will probably fail. This persists on real tasks, where it must estimate its own accuracy and causes miscalibration to increase while the agent's signal becomes less informative. Furthermore, we find that the LLM agent's decisions are coherent, but it systematically underestimates both how likely the user is to delegate and how secure its reputation is, resulting in less extreme behavior. Pricing the agent's reporting rule, we find that it destroys 68% of the gains from delegation, of which 71% is information the report no longer carries and no amount of user sophistication recovers. Overall, we establish confidence reporting under delegation as a strategic problem and provide a tractable basis for modeling, analyzing, and testing agent behavior.