Dynamic mechanism design in correlated environments

We consider the problem of implementing a principal's decision truthfully in a private-value, correlated environment in which agents receive information over time. This setting comprises a deviation from the literature of dynamic mechanism design that typically employs the assumption that the distribution of an agent's private signal is independent of other agents' private information history conditional on past public decisions. We derive sufficient conditions for designing monetary transfers that guarantee implementation of the desired policy in a periodic ex post incentive compatible equilibrium. For risk neutral agents in a finite state, finite action Markovian environment this set of sufficient conditions reduces to a finite set of linear inequalities. This is an appealing feature given that the agent is faced with a partial observation stochastic optimization problem with progressively increasing information state. The class of mechanisms considered in our methodology include the dynamic VCG algorithm that has been developed for the case where agents' dynamics are coupled only through the principal's decision. Besides implementing the desired policy, the principal may want to impose specifications on the expected revenue or model her uncertainty regarding her knowledge of agents' perceived environment. We show how our conditions for periodic ex post incentive compatibility can be incorporated as part of a robust optimization approach to policy implementation that takes these additional requirements into account.