Strategic Calibration in LLM Multi-Agent Systems: Audited Pivot Scoring for Truthful Elicitation
In large language model (LLM)-based multi-agent systems, reported confidence increasingly determines the allocation of scarce downstream attention, computation, and decision influence. This makes reporting strategic: an agent may overstate the relevance of its contribution even when its underlying belief is well calibrated. Existing calibration methods largely assume passive reporting and therefore do not address strategic incentives created when confidence determines downstream allocation. We formulate strategic calibration as a reporting-layer incentive problem and propose the Audited Pivot Scoring Mechanism (APSM). APSM offsets platform-controlled allocation benefits, uses inverse-propensity-weighted sparse audits, charges the Clarke pivot externality, and applies a strictly proper score. Under the stated model assumptions, truthful reporting is the unique expected-utility best response. We also characterize approximate execution and the audit-variance trade-off. Calculator-free experiments show that LLM agents inflate confidence under Top-$K$ incentives. With a shared agent-local utility interface, LLM agents reduce distortion under both Compensated Proper Scoring (CPS) and APSM. CPS achieves higher exact allocation match, whereas APSM yields lower Brier loss and numerically fewer cutoff crossings. Experiments further show that APSM enlarges the utility margin against allocation-changing deviations by $1.93\times$ and improves robustness under approximate execution. These results support incentive-aware elicitation as a distinct layer for reliable multi-agent coordination.