数字信道下对数比特率的分布式纳什均衡（NE）寻求
Distributed Nash Equilibrium Seeking with Logarithmic Bit Rates over Digital Channels
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中文总结 AI 辅助
本文针对分布式纳什均衡寻求问题，提出带时变缩放误差状态量化的基于无源性的算法，确定通信复杂度下界，实现比特率指数级降低，通过仿真验证理论结果。
中文摘要 AI 辅助
本文引入量化技术以降低分布式纳什均衡（NE）寻求问题中的通信复杂度，在数字信道上实现了比特率的指数级降低。分布式NE寻求算法的目标是通过网络中智能体间的迭代消息交换，协调网络博弈中的智能体趋向均衡。该分布式算法的计算复杂度关键取决于数字信道中的网络通信开销，这推动了通信减少机制的发展。针对此，我们提出了基于稀疏化和均匀量化的量化器，属于一类基于最终有界性的通用量化器。在此基础上，我们提出了带时变缩放误差状态量化的基于无源性的NE寻求算法（PBA-TEQ），并证明在充分条件下可实现线性收敛。此外，当在PBA-TEQ框架内采用标量量化器或贪婪量化器（两者均属于基于最终有界性的量化器）时，我们确定了通信复杂度的下界：每次传输需log₂(O(nd))比特率以实现无偏线性收敛，其中n为智能体数量，d为网络博弈决策状态的维度。数值仿真示例被提供以验证我们的理论结果。
英文摘要
This paper introduces quantization techniques to reduce the communication complexity in the distributed Nash equilibrium (NE) seeking problem, achieving an exponential reduction in bit rates over digital channels. The goal of distributed NE seeking algorithms is to coordinate agents in a network game toward equilibrium through iterative message exchanges among them via a communication network. The computational complexity of this distributed algorithm critically depends on network communication overhead in the digital channel, motivating the development of communication reduction mechanism. Regarding this, we proposed some quantizers based on sparsification and uniform quantization through a general class of ultimate-boundedness-based quantizers. Based on this, we propose a Passivity-Based NE seeking Algorithm with Time-varying scaling Error state Quantization (PBA-TEQ), and show that the linear convergence can be achieved under a sufficient condition. Moreover, when employing either the scalarization quantizer or the greedy quantizer, both belonging to the ultimate-boundedness-based quantizers, within the PBA-TEQ framework, we establish a lower bound on communication complexity of $\log_2(\mathcal{O}(nd))$ bit rates per transmission to achieve unbiased linear convergence, with $n$ being the number of agents and $d$ being the dimension of the decision state of the network game. Numerical simulation examples are provided to validate our theoretical results.
