Quadratic Funding Mechanisms for Artificial Intelligence Agriculture Weather Index Insurance Under Basis Risk and Strategic Reporting: A Computer Incentive-Compatibility Regret Bound

Weather index insurance for smallholder agriculture is undermined by basis risk, and the machine-learning models that now price such contracts are trained on farmer-reported outcomes that are themselves strategic. the present analysis formalises the resulting tripartite problem — a quadratic funding mechanism that aggregates farmer contributions to subsidise index-insurance premiums, an artificial-intelligence weather index trained on reported losses, and a regret bound that must hold under both basis risk and misreporting. The mechanism is modelled as a two-stage game in which farmers first choose a reporting strategy and then a coverage level, and the insurer commits to a quadratic matching rule. Under a proper-scoring assumption on the index, the paper derives an incentive-compatibility condition that separates the truthful-reporting region from the collusive-reporting region, and shows that the quadratic matching parameter controls the width of that region. A regret bound is then established for the insurer's cumulative subsidy loss relative to the truthful-reporting oracle; the bound scales with the square root of the horizon, with the basis-risk variance, and inversely with the matching parameter, and it degrades gracefully when the index is misspecified. The analysis is illustrated with a reanalysis of monthly air temperature at Nairobi, Kenya, from 2000 to 2023 (312 observations, mean 20.146 °C, warming trend 0.2477 °C per decade), which supplies the climatological basis-risk term. The contribution is a mechanism-design result that ties the quadratic funding parameter to an explicit regret guarantee, and a demonstration that the guarantee survives strategic reporting provided the index is trained on a proper scoring rule.