Min-Max优化问题（即，最大游戏）一直在吸引大量的注意力，因为它们适用于各种机器学习问题。虽然最近取得了重大进展，但迄今为止的文献已经专注于独立战略集的比赛;难以解决与依赖策略集的游戏的知识，可以被称为Min-Max Stackelberg游戏。我们介绍了两种一阶方法，解决了大类凸凹MIN-Max Stackelberg游戏，并表明我们的方法会聚在多项式时间。 Min-Max Stackelberg游戏首先由Wald研究，在Wald的Maximin模型的Posthumous名称下，一个变体是强大的优化中使用的主要范式，这意味着我们的方法同样可以解决许多凸起的稳健优化问题。我们观察到Fisher市场中竞争均衡的计算还包括Min-Max Stackelberg游戏。此外，我们通过在不同的公用事业结构中计算Fisher市场的竞争性均衡来证明我们的算法在实践中的功效和效率。我们的实验表明潜在的方法来扩展我们的理论结果，通过展示不同的平滑性能如何影响我们算法的收敛速度。

Development of guidance, navigation and control frameworks/algorithms for swarms attracted significant attention in recent years. That being said, algorithms for planning swarm allocations/trajectories for engaging with enemy swarms is largely an understudied problem. Although small-scale scenarios can be addressed with tools from differential game theory, existing approaches fail to scale for large-scale multi-agent pursuit evasion (PE) scenarios. In this work, we propose a reinforcement learning (RL) based framework to decompose to large-scale swarm engagement problems into a number of independent multi-agent pursuit-evasion games. We simulate a variety of multi-agent PE scenarios, where finite time capture is guaranteed under certain conditions. The calculated PE statistics are provided as a reward signal to the high level allocation layer, which uses an RL algorithm to allocate controlled swarm units to eliminate enemy swarm units with maximum efficiency. We verify our approach in large-scale swarm-to-swarm engagement simulations.