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We propose RACE, a report-based payment scheme for multihop wireless networks to stimulate node cooperation, regulate packet transmission, and enforce fairness. The nodes submit lightweight payment reports (instead of receipts) to the accounting center (AC) and temporarily store undeniable security tokens called Evidences. The reports contain the alleged charges and rewards without security proofs, e.g., signatures. The AC can verify the payment by investigating the consistency of the reports, and clear the payment of the fair reports with almost no processing overhead or cryptographic operations. For cheating reports, the Evidences are requested to identify and evict the cheating nodes that submit incorrect reports. Instead of requesting the Evidences from all the nodes participating in the cheating reports, RACE can identify the cheating nodes with requesting few Evidences. Moreover, Evidence aggregation technique is used to reduce the Evidences' storage area. Our analytical and simulation results demonstrate that RACE requires much less communication and processing overhead than the existing receipt-based schemes with acceptable payment clearance delay and storage area. This is essential for the effective implementation of a payment scheme because it uses micropayment and the overhead cost should be much less than the payment value. Moreover, RACE can secure the payment and precisely identify the cheating nodes without false accusations.