Efficient Mechanisms with Dynamic Populations and Dynamic Types

Abstract

We consider the truthful implementation of an efficient decision policy when agents have dynamic type and are periodically-inaccessible, with agents unable to report information or make payments while inaccessible. This concept of inaccessibility includes a model of arrival-departure dynamics as a special case. We generalize the dynamic VCG mechanism [Bergemann and V¨alim¨aki, 2008] to this environment, achieving within-period ex post incentive compatibility for agents with the same communication constraints as the center. In doing so, we offer a new proof of the correctness of the dynamic VCG mechanism, emphasizing its position within a family of dynamic Groves mechanisms. In considering the special case of an arrival-departure model with dynamic type, we obtain a mechanism that is efficient and within-period ex post incentive compatible for arrival processes in which future arrivals are conditionally independent of past arrivals given the actions of the center. The mechanism is shown to be payoff equivalent at arrival for agents with static types to the online VCG mechanism [Parkes and Singh, 2003], which satisfies a stronger ex post participation constraint than the dynamic VCG mechanism in such domains. In closing, we highlight a structural difficulty in extending the dynamic VCG mechanism to achieve an ex post no deficit, efficient mechanism in an environment with dynamic types and interdependent type transitions.