Robust Dynamic Mechanism Design

In situations in which the social planner has to make several decisions over time, before agents have observed all the relevant information, static mechanisms may not su¢ ce to induce agents to reveal their information truthfully. This paper focuses on questions of partial and full implementation in dynamic mechanisms, when agents’ beliefs are unknown to the designer (hence the term “robust”). It is shown that a social choice function (SCF) is (partially) implementable for all models of beliefs if and only if it is ex-post incentive compatible. Furthermore, in environments with single crossing preferences, strict ex-post incentive compatibility and a “contraction property” are su¢ cient to guarantee full robust implementation. This property limits the interdependence in agents’valuations. Full robust implementation requires that, for all models of agents beliefs, all the perfect Bayesian equilibria of a mechanism induce outcomes consistent with the SCF. This paper shows that, for a weaker notion of equilibrium and for a general class of dynamic games, the set of all such equilibria can be computed by means of a “backwards procedure”which combines the logic of rationalizability and backward induction reasoning. It thus provides foundation to a tractable approach to the implementation question, allowing at the same time stronger implementation results.