We study binary coordination games over graphs under log-linear learning when neighbor actions are conveyed through explicit noisy communication links. Each edge is modeled as either a binary symmetric channel (BSC) or a binary erasure channel (BEC). We analyze two operational regimes. For binary symmetric and binary erasure channels, we provide a structural characterization of the induced learning dynamics. In a fast-communication regime, agents update using channel-averaged payoffs; the resulting learning dynamics coincide with a Gibbs sampler for a scaled coordination potential, where channel reliability enters only through a scalar attenuation coefficient. In a snapshot regime, agents update from a single noisy realization and ignore channel statistics; the induced Markov chain is generally nonreversible, but admits a high-temperature expansion whose drift matches that of the fast Gibbs sampler with the same attenuation. We further formalize a finite-$K$ communication budget, which interpolates between snapshot and fast behavior as the number of channel uses per update grows. This viewpoint yields a communication-theoretic interpretation in terms of retransmissions and repetition coding, and extends naturally to heterogeneous link reliabilities via effective edge weights. Numerical experiments illustrate the theory and quantify the tradeoff between communication resources and steady-state coordination quality.

翻译：我们研究了在图结构上通过显式噪声通信链路传递邻居动作时，基于对数线性学习的二元协调博弈。每条边被建模为二元对称信道（BSC）或二元擦除信道（BEC）。我们分析了两种运行机制。针对二元对称信道和二元擦除信道，我们对所诱导的学习动力学进行了结构刻画。在快速通信机制下，智能体使用信道平均收益进行更新；由此产生的学习动力学与一个缩放协调势的吉布斯采样器一致，其中信道可靠性仅通过一个标量衰减系数体现。在快照机制下，智能体基于单次噪声实现进行更新并忽略信道统计特性；所诱导的马尔可夫链通常不可逆，但其允许一个高温展开，其漂移项与具有相同衰减系数的快速吉布斯采样器相匹配。我们进一步形式化了一个有限-$K$ 通信预算，该预算随着每次更新所使用的信道次数增加而在快照行为与快速行为之间平滑过渡。这一视角从重传和重复编码的角度提供了一种通信理论的解释，并通过有效边权重自然地扩展到异构链路可靠性场景。数值实验验证了理论结果，并量化了通信资源与稳态协调质量之间的权衡关系。