Models of choice where agents see others as less sophisticated than themselves have significantly different, sometimes more accurate, predictions in games than does Nash equilibrium. When it comes to mechanism design, however, they turn out to have surprisingly similar implications. This paper...

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term...

It is well known that a social choice function is truthfully implementable in Bayesian Nash equilibrium if and only if it is incentive compatible. However, in general it is not possible to rule out other equilibrium outcomes, and additional conditions, e.g., Bayesian monotonicity, are needed to...

We consider robust virtual implementation, where robustness is the requirement that implementation succeed in all type spaces consistent with a given payoff type space as well as with a given space of first-order beliefs about the other agents’ payoff types. This last bit, which constitutes...

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions...

We characterize full implementation of social choice sets in mixedstrategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It...

We consider mechanism design in contexts in which agents exhibit bounded depth of reasoning (level k) instead of rational expectations. We use simple direct mechanisms, in which agents report only first-order beliefs. While level 0 agents are assumed to be truth tellers, level k agents...

Models of choice where agents see others as less sophisticated than themselves have significantly different, sometimes more accurate, predictions in games than does Nash equilibrium. When it comes to mechanism design, however, they turn out to have surprisingly similar implications. This paper...

We consider mechanism design in contexts in which agents exhibit bounded depth of reasoning (level k ) instead of rational expectations. We use simple direct mechanisms, in which agents report only first-order beliefs. While level 0 agents are assumed to be truth tellers, level k agents...

We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It...