The Theory of Implementation When the Planner Is a Player
In this paper we study a situation were the planner cannot commit to a mechanism and the outcome function is substituted by the planner herself. We assume 1) agents have complete information and play simultaneously; and 2) given the messages announced by the agents, the planner reacts in an optimal way given her beliefs. This transforms the implementation problem into a signaling game. We derive necessary and sufficient conditions for interactive implementation under different restrictions on the planner's out-of-equilibrium beliefs. We compare our results to standard results on Nash implementation.
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