In dynamic mechanism design literature, one critical aspect has been typically ignored-the agents' periodic participation, which they can adapt and plan strategically. We propose a framework for dynamic principal-multiagent problems, augmenting the classic model by incorporating agents' periodic coupled decisions on participation and regular action selections. The principal faces adverse selection and designs a mechanism comprising a task policy profile (defining evolving agent action menus), a coupling policy profile (affecting agent utilities), and an off-switch function profile (assigning rewards or penalties upon agent withdrawal). Firstly, we introduce payoff-flow conservation-a sufficient condition to ensure dynamic incentive compatibility for regular actions. Secondly, we formulate a unique process, persistence transformation, which integrates task policy's implicit functions, enabling a closed-form off-switch function derivation, hence securing sufficient conditions for agents' coupled decisions' incentive compatibility, aligning with the principal's preferences. Thirdly, we go beyond the traditional envelope theorem by presenting a necessary condition for incentive compatibility, leveraging the coupled optimality of principal-desired actions. This approach helps explicitly formulate both the coupling and off-switch functions. Finally, we establish envelope-like conditions exclusively on the task policies, facilitating the application of the first-order approach.

翻译：在动态机制设计文献中，一个关键方面通常被忽视——智能体的周期性参与，它们能够对此进行战略性的适应和规划。我们提出了一个动态主方-多智能体问题的框架，通过引入智能体在参与和常规行动选择上的周期性耦合决策，对经典模型进行了扩充。主方面临逆向选择，并设计了一个机制，该机制包含任务策略轮廓（定义演变的智能体行动菜单）、耦合策略轮廓（影响智能体效用）以及退出开关函数轮廓（在智能体退出时分配奖励或惩罚）。首先，我们引入了支付流守恒——这是确保常规行动动态激励相容的充分条件。其次，我们制定了一个独特的过程，即持久性变换，它整合了任务策略的隐函数，使得能够推导出闭合形式的退出开关函数，从而为智能体耦合决策的激励相容性提供了充分条件，并使之与主方的偏好保持一致。第三，我们超越了传统的包络定理，通过利用主方期望行动的耦合最优性，提出了激励相容的必要条件。这种方法有助于显式地表述耦合函数和退出开关函数。最后，我们专门针对任务策略建立了类似包络的条件，以促进一阶方法的应用。