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We study the design of decision-making mechanism for resource allocationsover a multi-agent system in a dynamic environment. Agents' privately observedpreference over resources evolves over time and the population is dynamic dueto the adoption of stopping rules. The proposed model designs the rules ofencounter for agents participating in the dynamic mechanism by specifying anallocation rule and three payment rules to elicit agents' coupled decisionmakings of honest preference reporting and optimal stopping over multipleperiods. The mechanism provides a special posted-price payment rule thatdepends only on each agent's realized stopping time to directly influence thepopulation dynamics. This letter focuses on the theoretical implementability ofthe rules in perfect Bayesian Nash equilibrium and characterizes necessary andsufficient conditions to guarantee agents' honest equilibrium behaviors overperiods. We provide the design principles to construct the payments in terms ofthe allocation rules and identify the restrictions of the designer's ability toinfluence the population dynamics. The established conditions make thedesigner's problem of finding multiple rules to determine an optimal allocationrule.

Implementability of Honest Multi-Agent Sequential Decision-Making with Dynamic Population