We characterize zonal ancillary market coupling relying on noncooperative game theory. To that purpose, we formulate the ancillary market as a multi-leader single follower bilevel problem, that we subsequently cast as a generalized Nash game with side constraints and nonconvex feasibility sets. We determine conditions for equilibrium existence and show that the game has a generalized potential game structure. To compute market equilibrium, we rely on two exact approaches: an integrated optimization approach and Gauss-Seidel best-response, that we compare against multi-agent deep reinforcement learning. On real data from Germany and Austria, simulations indicate that multi-agent deep reinforcement learning achieves the smallest convergence rate but requires pretraining, while best-response is the slowest. On the economics side, multi-agent deep reinforcement learning results in smaller market costs compared to the exact methods, but at the cost of higher variability in the profit allocation among stakeholders. Further, stronger coupling between zones tends to reduce costs for larger zones.

翻译：本文基于非合作博弈论对区域辅助服务市场耦合机制进行理论刻画。为此，我们将辅助服务市场建模为多领导者-单跟随者的双层规划问题，进而将其转化为带侧约束与非凸可行集的广义纳什博弈。我们确立了均衡存在的条件，并证明该博弈具有广义势博弈结构。为计算市场均衡，我们采用两种精确求解方法：集成优化方法与高斯-赛德尔最优响应策略，并将其与多智能体深度强化学习进行对比。基于德国与奥地利实际数据的仿真表明：多智能体深度强化学习收敛速度最慢但需预训练，最优响应策略收敛速度最慢。从经济学角度分析，多智能体深度强化学习相较于精确方法能实现更低的市场总成本，但代价是利益相关方之间的利润分配具有更高波动性。此外，区域间更强的耦合效应倾向于降低较大区域的运营成本。