We consider an allocation problem with indivisible goods, and provide a necessary and sufficient condition for weak Maskin monotonic allocation rules under non-wastefulness. The condition is based on robustness to group manipulation. Specifically, we introduce a new condition called the no improvement property of unmatched agents which means that unmatched agents cannot be strictly better off through any group manipulation. We show that a non-wasteful allocation rule satisfies weak Maskin monotonicity if and only if it satisfies the no improvement property of unmatched agents and weak group strategy-proofness. In addition, together with our result and that of Kojima and Manea (Econometrica 78:633–653, 2010), the deferred acceptance (DA) rules with acceptant substitutable priorities are characterized based on the conditions related to robustness to group manipulation.
ASJC Scopus subject areas