  We study the design of decision-making mechanism for resource allocations
over a multi-agent system in a dynamic environment. Agents' privately observed
preference over resources evolves over time and the population is dynamic due
to the adoption of stopping rules. The proposed model designs the rules of
encounter for agents participating in the dynamic mechanism by specifying an
allocation rule and three payment rules to elicit agents' coupled decision
makings of honest preference reporting and optimal stopping over multiple
periods. The mechanism provides a special posted-price payment rule that
depends only on each agent's realized stopping time to directly influence the
population dynamics. This letter focuses on the theoretical implementability of
the rules in perfect Bayesian Nash equilibrium and characterizes necessary and
sufficient conditions to guarantee agents' honest equilibrium behaviors over
periods. We provide the design principles to construct the payments in terms of
the allocation rules and identify the restrictions of the designer's ability to
influence the population dynamics. The established conditions make the
designer's problem of finding multiple rules to determine an optimal allocation
rule.
