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：我们研究了具有全行秩等式约束的广义博弈，并给出了关联KKT算子强单调性的简明证明。这使我们能够证明由此产生的原-对偶伪梯度动力学变分均衡的线性收敛性。接着，我们提出了一种在部分决策信息下针对聚合博弈具有线性收敛保证的全分布式算法。基于这些结果，我们建立了具有时变成本函数和约束的博弈中在线广义纳什均衡搜索的稳定性性质。最后，我们以点对点能源市场中的经济调度问题为例，通过数值实验验证了所得结论。