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

Abstract

This paper studies dynamic mechanism design in a Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent’s private information, referred to as state, evolves over time. The agent makes decisions of whether to stop or continue and what to report at each period. The principal, on the other hand, chooses decision rules consisting of an allocation rule and a set of payment rules to maximize her ex-ante expected payoff. In order to influence the agent’s stopping decision, one of the terminal payment rules is posted-price, i.e., it depends only on the realized stopping time of the agent. This work focuses on the theoretical design regime of the dynamic mechanism design when the agent makes coupled decisions of reporting and stopping. A dynamic incentive compatibility constraint is introduced to guarantee the robustness of the mechanism to the agent’s strategic manipulation. A sufficient condition for dynamic incentive compatibility is obtained by constructing the payment rules in terms of a set of functions parameterized by the allocation rule. The payment rules are then pinned down up to a constant in terms of the allocation rule by deriving a first-order condition. We show cases of relaxations of the principal’s mechanism design problem and provide an approach to evaluate the loss of robustness of the dynamic incentive compatibility when the problem solving is relaxed due to analytical intractability. A case study is used to illustrate the theoretical results.