Measuring Inter-Agent Trust: A Memoryless-Anchor Instrument for Interactive, Non-Stationary Evaluation

Benchmarks usually score a model on a fixed battery of independent items. Inter-agent trust (how much one LLM agent relies on another) fits that format badly: it exists only in interaction, is path-dependent (built from a history, so the observations are not independent), and concerns a partner whose reliability can change over time. We treat measuring it as a methodological problem and contribute an instrument with an explicit validity argument. The construct is operationalized in the tradition of experimental economics: trust is read from a costly choice, not a questionnaire. In a cooperative game, verifying a teammate spends a scarce resource while trusting a wrong answer is fatal, so reduced verification is an incentive-compatible indicator of trust. The instrument's core is a matched-null anchor: each model is compared against a memoryless copy of itself that reasons identically within a game but carries no cross-game history, isolating the history-driven signal from baseline temperament. We argue construct validity (the indicator is history-dependent, partner-specific, costly, and separable from competence) and discriminant validity (we rule out cost-cutting, task learning, fixed caution, and pure evidence-counting). Because observations are sequentially dependent, all uncertainty uses cluster bootstraps over the correct unit of analysis. Applied to six frontier snapshots under controlled non-stationarity, the instrument is sensitive (it detects 60–85% trust-formation effects), discriminating (it separates models other metrics rank together), and reveals a measurement-relevant anomaly: distrust tracks the coherence of a failure history, not just its evidence, so clustered failures register far stronger than the same failures spread apart. We close with the open measurement problems an interactive, gameable instrument raises.