Robust group strategy-proofness

Strategy-proofness (SP) is a sought-after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex-post stages. Group strategy-proofness (GSP), however, is a notion that is applied to the ex-post stage but not to the interim stage. Thus, we propose a new notion of GSP, coined robust group strategy-proofness (RGSP), which ensures that no group benefits by deviating from truthtelling at the interim stage. We show for the provision of a public good that the Minimum Demand rule (Serizawa, 1999) satisfies RGSP when the production possibilities set satisfies a particular topological property. In the problem of allocating indivisible objects, an acyclicity condition on the priorities is both necessary and sufficient for the Deferred Acceptance rule to satisfy RGSP, but is only necessary for the Top Trading Cycles rule. For the allocation of divisible private goods among agents with single-peaked preferences (Sprumont, 1991), only free disposal, group replacement monotonic rules within the class of sequential allotment rules satisfy RGSP.