In traditional blockchain networks, transaction fees are only allocated to full nodes (i.e., miners) regardless of the contribution of forwarding behaviors of light nodes. However, the lack of forwarding incentive reduces the willingness of light nodes to relay transactions, especially in the energy-constrained Mobile Ad Hoc Network (MANET). This paper proposes a novel dual auction mechanism to allocate transaction fees for forwarding and validation behaviors in the wireless blockchain network. The dual auction mechanism consists of two auction models: the forwarding auction and the validation auction. In the forwarding auction, forwarding nodes use Generalized First Price (GFP) auction to choose transactions to forward. Besides, forwarding nodes adjust the forwarding probability through a no-regret algorithm to improve efficiency. In the validation auction, full nodes select transactions using Vickrey-Clarke-Grove (VCG) mechanism to construct the block. We prove that the designed dual auction mechanism is Incentive Compatibility (IC), Individual Rationality (IR), and Computational Efficiency (CE). Especially, we derive the upper bound of the social welfare difference between the social optimal auction and our proposed one. Extensive simulation results demonstrate that the proposed dual auction mechanism decreases energy and spectrum resource consumption and effectively improves social welfare without sacrificing the throughput and the security of the wireless blockchain network.

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