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略——即主体（智能体）的周期性参与行为，他们能够策略性地适应和规划这一过程。我们提出了一个面向动态主从式多智能体问题的框架，通过引入主体在参与决策与常规行动选择上的周期性耦合决策，对经典模型进行了扩展。委托人面临逆向选择问题，需设计包含以下三部分的机制：任务策略档案（定义演化的智能体行动菜单）、耦合策略档案（影响智能体效用）及退出开关函数档案（在智能体退出时分配奖励或惩罚）。首先，我们提出收益流守恒条件——这是确保常规行动动态激励相容的充分条件。其次，我们构建了独特的“持久性变换”过程，该过程整合了任务策略的隐式函数，可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充分条件，使其与委托人的偏好保持一致。第三，我们超越传统包络定理，通过利用委托人期望行动的耦合最优性，提出了激励相容的必要条件。该方法有助于显式地构建耦合函数与退出开关函数。最后，我们建立了仅依赖于任务策略的类包络条件，从而促进了一阶方法的适用。