Selfrejecting mechanisms Abstract   In mechanism design problems where the outside option is a game, a version of the intuitive criterion restricts beliefs formed offpath in case of disagreement, and thus credible punishments for rejecting to participate. However, for virtual implementation, participation constraints can be relaxed by xe2x80x9cdesigningxe2x80x9d beliefs following disagreement using selfrejections: with a small probability that depends on the reported type profile, a mediator rejects the agreement in a way that is indistinguishable from rejection by an agent. Participation constraints can be further relaxed if the mediator makes private recommendations before the outside game is played. Any punishment (by all players except the rejector) such that each playertype is never asked to use an action he does not use in any Bayesian solution of the outside game is a credible punishment.

On nonmonotonic strategic reasoning Abstract   Strongxcex94Rationalizability introduces firstorder belief restrictions in the analysis of forward induction reasoning. Without actual restrictions, it coincides with Strong Rationalizability (Battigalli 2003, Battigalli and Siniscalchi 2003). These solution concepts are based on the notion of strong belief (Battigalli and Siniscalchi 2002). The nonmonotonicity of strong belief implies that the predictions of Strongxcex94Rationalizability can be inconsistent with Strong Rationalizability. I show that Strongxcex94Rationalizability refines Strong Rationalizability in terms of outcomes when the restrictions correspond to belief in a distribution over terminal nodes. Moreover, under such restrictions, the epistemic priority between rationality and belief restrictions is irrelevant for the predicted outcomes.