We address multi-agent Stackelberg settings involving many leaders and followers. In order to effectively model this kind of interactions, we extend the idea of commitment to correlated strategies to Stackelberg games with multiple leaders and followers. Correlation can be easily implemented by resorting to a device that sends signals to the players, and it also enables the leaders to reach better solutions than those achieved by committing independently. In this setting, a crucial question is how the leaders agree on a correlated-strategy commitment. To this end, we introduce a preliminary agreement stage that implements a natural non-cooperative negotiation protocol. The protocol proposes a correlated strategy to the leaders, who can then decide, in turn, whether to participate in the commitment or defect from it by losing the possibility of being part of the agreement. The goal is to design stable agreements in which no leader defects. We distinguish three solution concepts on the basis of the constraints that they enforce on the agreement reached by the leaders. We provide a comprehensive study of the properties of our solution concepts, in terms of existence, relation with other solution concepts, and computational complexity. As for the computational analysis, we prove that our solutions can be computed in polynomial time for certain classes of succinctly represented games. Interestingly, our results show that, in these games, introducing the agreement stage does not make computing equilibria a more challenging task, as finding a solution in our setting is as hard as computing an optimal correlated equilibrium.

我们解决涉及许多领导者和追随者的多代理 Stackelberg 设置。为了有效地模拟这种交互，我们将承诺相关策略的想法扩展到具有多个领导者和追随者的 Stackelberg 游戏。借助向玩家发送信号的设备，可以轻松实现关联，并且还使领导者能够找到比独立提交更好的解决方案。在这种情况下，一个关键问题是领导者如何就相关战略承诺达成一致。为此，我们引入了初步协议阶段它实现了一个自然的非合作协商协议。该协议向领导者提出了一个相关的策略，然后领导者可以决定是参与承诺还是通过失去成为协议一部分的可能性而违背承诺。目标是设计没有领导者缺陷的稳定协议。我们根据对领导人达成的协议施加的约束来区分三个解决方案概念。我们全面研究了我们的解决方案概念的属性，包括存在性、与其他解决方案概念的关系以及计算复杂性。至于计算分析，我们证明了我们的解决方案可以在多项式时间内计算出某些类别的简洁表示的游戏。有趣的是，我们的结果表明，在这些游戏中，不要让计算均衡成为一项更具挑战性的任务，因为在我们的设置中找到解决方案与计算最佳相关均衡一样困难。