In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient steps and an averaging procedure. Each agent uses estimates of competitors' actions obtained solely from local neighbor interactions, in a directed communication network. Unlike previous approaches that rely on (strong) monotonicity assumptions, this work establishes the convergence towards a NE under a diagonal dominance property of the pseudo-gradient mapping, that can be checked locally by the agents. Further, this condition is physically interpretable and of relevance for many applications, as it suggests that an agent's objective function is primarily influenced by its individual strategic decisions, rather than by the actions of its competitors. In virtue of a novel block-infinity norm convergence argument, we provide explicit bounds for constant step-size that are independent of the communication structure, and can be computed in a totally decentralized way. Numerical simulations on an optical network's power control problem validate the algorithm's effectiveness.

翻译：本文针对部分决策信息下非合作凸博弈中的纳什均衡求解问题展开研究。我们提出一种分布式算法，其中每个智能体通过投影梯度步骤与平均化过程来调整自身策略。每个智能体仅利用有向通信网络中局部邻居交互获取的对手行动估计值。与以往依赖（强）单调性假设的方法不同，本文在伪梯度映射满足对角占优特性的条件下建立了向纳什均衡的收敛性，该条件可由智能体局部验证。此外，该条件具有物理可解释性且与诸多应用场景相关，因为它表明智能体的目标函数主要受其个体战略决策影响，而非竞争对手的行动。通过引入新颖的块无穷范数收敛论证，我们给出了与通信结构无关的恒定步长显式界，该步长可完全以分布式方式计算。光学网络功率控制问题的数值仿真验证了该算法的有效性。