Multiagent Incentive Design for Dynamic Task Delegation with Off-Menu Actions

Surprisingly, the literature on dynamic mechanism seems to give relatively less attention to agents' dynamic participation, particularly regarding incentive compatibility with respect to these decisions. This addresses this gap by studying a dynamic mechanism design problem of task delegation. We expand upon the classic state mechanism model by incorporating agents' dual decisions concerning participation (off-menu actions) and regular action selections across multiple periods. The principal faces adverse selection, as agents receive private information over time that remains unobserved by the principal, and designs a mechanism of a task policy profile, which outlines the evolution of available action menus for agents; a coupling policy profile that directly impacts agents' utilities; and an off-switch function profile that assigns compensation or penalties if an agent withdraws. First, we present a sufficient condition called ``payoff-flow conservation" for ensuring dynamic incentive compatibility concerning regular actions. Second, we propose a unique process called persistence transformation, which allows us to derive a closed-form formulation for each off-switch function based on the task policy and carrier functions. This enables us to obtain a sufficient condition for the incentive-compatible concerning agents' combined decisions of off-menu and regular actions, aligning with the principal's preferences. Third, we provide a necessary condition for incentive compatibility that goes beyond canonical envelope conditions by leveraging the coupled optimality of the principal-desired off-menu and regular actions. This method allows us to obtain a set of sufficient conditions for incentive compatibility by pinning down an explicit expression for each carrier function, thereby determining the precise closed-form formulations of both the coupling functions and the off-switch functions.