Robust Virtual Implementation under Common Strong Belief in Rationality

Robust virtual implementation asks if a social goal can be approximately achieved if merely the agents’ rationality is commonly believed in. Bergemann and Morris (2009b) show that static mechanisms cannot robustly virtually implement any non-constant social goal if preferences are sufficiently interdependent. Without any knowledge of how agents revise their beliefs this impossibility result extends to dynamic mechanisms, and focusing on static mechanisms is without loss of generality. In contrast, this paper shows that admitting dynamic mechanisms leads to considerable gains if agents commonly believe in rationality “as long as possible.” We illustrate this in private consumption environments with discrete payoff types and generic valuation functions. In such environments, dynamic mechanisms can robustly virtually implement all ex-post incentive compatible social goals regardless of the level of preference interdependence. This result derives from the key insight that under common strong belief in rationality (Battigalli and Siniscalchi, 2002), dynamic mechanisms can almost always distinguish all payoff type profiles by their strategic choices. Notably, dynamic mechanisms can robustly virtually implement the efficient allocation of an object even if static mechanisms cannot.