We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

翻译：我们研究具有完整行秩平等约束的广义博弈，并提供了一个令人惊奇地简单的强单调性证明方法。这使我们能够展示由原始-对偶伪梯度动力学的变分均衡出发的线性收敛。然后，我们提出了一种完全分布式算法，该算法在部分决策信息下保证线性收敛率，用于汇总游戏。基于这些结果，我们建立起针对时变代价函数和约束的在线广义纳什均衡搜索的稳定性。最后，我们通过对等能源市场中的经济调度问题进行数值分析来说明我们的研究结果。