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In dynamic mechanism design literature, one critical aspect has beentypically ignored-the agents' periodic participation, which they can adapt andplan strategically. We propose a framework for dynamic principal-multiagentproblems, augmenting the classic model by incorporating agents' periodiccoupled decisions on participation and regular action selections. The principalfaces adverse selection and designs a mechanism comprising a task policyprofile (defining evolving agent action menus), a coupling policy profile(affecting agent utilities), and an off-switch function profile (assigningrewards or penalties upon agent withdrawal). Firstly, we introduce payoff-flowconservation-a sufficient condition to ensure dynamic incentive compatibilityfor regular actions. Secondly, we formulate a unique process, persistencetransformation, which integrates task policy's implicit functions, enabling aclosed-form off-switch function derivation, hence securing sufficientconditions for agents' coupled decisions' incentive compatibility, aligningwith the principal's preferences. Thirdly, we go beyond the traditionalenvelope theorem by presenting a necessary condition for incentivecompatibility, leveraging the coupled optimality of principal-desired actions.This approach helps explicitly formulate both the coupling and off-switchfunctions. Finally, we establish envelope-like conditions exclusively on thetask policies, facilitating the application of the first-order approach.

A Dynamic Adverse Selection Multiagent Model with Off-Menu Actions