Subgame-Perfect Implementation Under Value Perturbations

We consider the robustness of extensive form mechanisms when common knowledge of the state of Nature is relaxed to common p-beliefs about it. We show that with even an arbitrarily small amount of such uncertainty, the Moore-Repullo mechanism does not yield (even approximately) truthful revelation and in addition there are sequential equilibria with undesirable outcomes. More generally, we show that any extensive form mechanism is fragile in the sense that if a non-monotonic social objective can be implemented with this mechanism, then there are arbitrarily small common p-belief value perturbations under which an undesirable sequential equilibrium exists.

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