Damage-based cost recovery and equitable tolling: a Shapley value model linking ESAL factors to highway fee structures in Nigeria

Nigeria's reintroduction of toll gates on federal highways through public-private partnerships (PPPs) aims to address chronic funding gaps for road rehabilitation and maintenance. However, the current flat-rate tolling policy is inequitable because vehicle types impose widely varying degrees of pavement damage, largely driven by axle load configuration [1]. This study develops and applies a differentiated tolling framework for the Abuja–Lokoja highway using cooperative game theory, specifically the Shapley value method [2, 3], to allocate maintenance costs proportionally across vehicle categories based on their marginal damage contributions. Traffic volume data, axle configurations, and Equivalent Single Axle Load (ESAL) factors for five vehicle categories (2A, 3A, 4A, 5A, 6A) were obtained from Federal agencies, namely: Federal Roads maintenance Agency (FERMA), Federal Roads Safety Corps (FRSC), and Federal Ministry of Works (FMW) [4, 5, 6]. The Shapley value model was applied to compute equitable toll rates ranging from ₦9,932 (≈$6.62) for two-axle vehicles to ₦72,629 (≈$48.42) for six-axle trucks, reflecting a 7.3:1 damage ratio. Coalition analysis revealed that six-axle vehicles alone contribute 52.10% of the total pavement damage, while representing only 39.8% of the traffic volume. In contrast, the government's announced flat-rate structure (₦500-₦1,600) significantly underprices heavy vehicles and fails to recover maintenance costs. The proposed framework demonstrates that damage-based tolling enhances equity, ensures sustainable cost recovery, and creates proper economic incentives for the preservation of infrastructure. Implementation requires electronic toll collection (ETC) and weigh-in-motion (WIM) technologies, supported by transparent governance mechanisms to prevent revenue misappropriation. These findings provide an actuarially efficient and scientifically defensible foundation for an equitable PPP toll policy in Nigeria and similar developing country contexts.