A necessary and sufficient condition for weak Maskin monotonicity in an allocation problem with indivisible goods

We consider an allocation problem with indivisible goods, and characterize weak Maskin monotonic allocation rules based on the robustness to group manipulation. Specifically, we introduce a new condition called unimprovement 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 unimprovement property of unmatched agents and weak group strategy-proofness. ∗Department of Social Engineering, Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Mailbox W9-96, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552 Japan; E-mail: [email protected] †Department of Social Engineering, Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Mailbox W9-96, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552 Japan; E-mail: [email protected]