Metering Truthfulness as an Inspection Game: Optimal Audit, Stake, and Sensor Accuracy in Tokenised Energy Markets

Abstract

A tokenised energy market settles payment against metered dispatch, but the meter reading is the prosumer's private information: a self-interested prosumer can report more energy than it supplied and be paid for the difference. The companion papers in this programme assume meter integrity — truthful reporting — and build settlement, participation, and delivery contracts on top of it. This paper derives the verification contract that makes the assumption hold. A prosumer dispatches a quantity it observes privately and reports a possibly inflated figure to the settlement layer; the grid-telemetry layer can audit a report at a cost, detecting a discrepancy with a probability that reflects sensor accuracy, and a detected misreport forfeits a posted verification stake. We treat the audit probability, the stake, and the sensor accuracy as the designer's instruments and characterise the verification that makes truthful reporting weakly dominant at minimum cost. The baseline assumes a margin-independent detection probability and one-sided audit error (false negatives possible, false positives excluded); both are stated and the general margin-dependent condition is given. First, truthful reporting is weakly dominant if and only if the expected forfeiture covers the largest gain from admissible over-reporting, αφB ≥ Pm̄ (strict under strict inequality), where α is the audit probability, φ the per-audit detection probability, B the stake, and m̄ the largest admissible over-report; with a one-unit maximum this is αφB ≥ P (Proposition 1). Second, along this deterrence frontier the audit probability is α = Pm̄/(φB), and once the stake is itself chosen against its capital carry the least-cost interior contract is B* = √(κPm̄/(ρφ)), α* = √(ρPm̄/(κφ)), total cost 2√(ρκPm̄/φ), all decreasing in detection accuracy, so accurate telemetry drives the audit rate, the stake, and the cost down together (Theorem 1). Third, sensor accuracy is itself a procurable instrument with a convex capital cost, and the cost-minimising accuracy equates marginal sensor capital cost to the marginal audit-opex saving, a capex–opex frontier between better meters and more auditing (Proposition 2). Fourth, the per-report enforcement αφB is exactly the meter-integrity guarantee the companion papers assume; truthful reporting is weakly dominant on the binding frontier and strict under an arbitrarily small slack, so the reported quantity equals the dispatched quantity, discharging that assumption from primitives and closing the stack at its base (Proposition 3). Full proofs are in the online appendix.