Many important dynamic mechanisms are menu mechanisms, where at each history an agent selects from a menu of his possible assignments. We investigate when a menu mechanism and a convention| which species a strategy for each agent given his type | together form an ex-post perfect implementation of a rule. We find that if (i) each agent's possible preferences over his assignments include all strict rankings; (ii) the rule is strategy-proof, (iii) an agent can never select an assignment twice along any play; (iv) the convention species that each agent always selects a most-preferred assignment, and that subject to this he breaks ties consistently; and (v) the rule's outcome is always reached when agents follow the convention; then we have an ex-post perfect implementation of the rule (Theorem 1). If, moreover, preferences are always strict and the rule is group strategy-proof, then we have a full subgame perfect implementation of the rule (Theorem 2). In the event of such double implementation, each ex-post perfect convention is compatible with the rule.
