In traditional public blockchain networks, transaction fees are only allocated to full nodes (i.e., miners). However, the lack of relay rewards reduces the willingness of light nodes to relay transactions, especially in the energy-constrained complex wireless network. This paper proposes a novel dual auction mechanism to allocate transaction fees for relay and validation behaviors in the wireless blockchain network. The dual auction mechanism consists of two sub-auction stages: the relay sub-auction and the validation sub-auction. In the relay sub-auction, relay nodes choose transactions based rewards to forward. Besides, relay nodes adjust the relaying probability through a no-regret algorithm to improve efficiency. In the validation sub-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). We also 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 bandwidth resource consumption and effectively improves social welfare without sacrificing the throughput and the security of the wireless blockchain network.

翻译：传统公有区块链网络中，交易费用仅分配给全节点（即矿工）。然而，中继奖励的缺失降低了轻节点中继交易的意愿，尤其在能量受限的复杂无线网络中更为显著。本文针对无线区块链网络中的中继与验证行为，提出一种新颖的双重拍卖机制以分配交易费用。该双重拍卖机制包含两个子阶段：中继子拍卖与验证子拍卖。在中继子拍卖中，中继节点基于奖励选择待转发的交易，并通过无憾算法调整中继概率以提升效率。在验证子拍卖中，全节点采用Vickrey-Clarke-Grove（VCG）机制选择交易以构建区块。我们证明了所设计的双重拍卖机制满足激励相容性（IC）、个体理性（IR）与计算效率（CE）。此外，我们推导了社会最优拍卖与所提方案之间社会福利差异的上界。大量仿真结果表明，所提出的双重拍卖机制在不牺牲无线区块链网络吞吐量与安全性的前提下，能够降低能量与带宽资源消耗，并有效提升社会福利。