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This paper studies dynamic mechanism design in a quasilinear Markovianenvironment and analyzes a direct mechanism model of a principal-agentframework in which the agent is allowed to exit at any period. We consider thatthe agent's private information, referred to as state, evolves over time. Theagent makes decisions of whether to stop or continue and what to report at eachperiod. The principal, on the other hand, chooses decision rules consisting ofan allocation rule and a set of payment rules to maximize her ex-ante expectedpayoff. In order to influence the agent's stopping decision, one of theterminal payment rules is posted-price, i.e., it depends only on the realizedstopping time of the agent. We define the incentive compatibility in thisdynamic environment in terms of Bellman equations, which is then simplified byestablishing a one-shot deviation principle. Given the optimality of thestopping rule, a sufficient condition for incentive compatibility is obtainedby constructing the state-dependent payment rules in terms of a set offunctions parameterized by the allocation rule. A necessary condition isderived from envelope theorem, which explicitly formulates the state-dependentpayment rules in terms of allocation rules. A class of monotone environment isconsidered to characterize the optimal stopping by a threshold rule. Theposted-price payment rules are then pinned down in terms of the allocation ruleand the threshold function up to a constant. The incentive compatibilityconstraints restrict the design of the posted-price payment rule by a regularcondition.

On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment