The Local-global Equivalence on General Networks

Strategy-proofness is an incentive property requiring that no (preference) type gain by reporting any other type in a prespecified domain of admissible types. The “local-global equivalence (LGE)” refers to the equivalence of strategy-proofness and “local” strategy-proofness, which requires immunity to misrepresentation assuming that an agent is constrained to report “local” types relative to his true type. Generalizing an existing framework, we allow the notion of localness to be arbitrary and directed and hence manipulation opportunities to be asymmetric across types. We identify two conditions, each of which characterizes the networks satisfying LGE: (i) strong connectedness, a refined notion of connectedness; and (ii) Property DL, a directed-network adaptation of Property L by Kumar et al. (2021a). This characterization also helps reveal conditions for the random version of LGE (the equivalence of strategy-proofness and local strategy-proofness for random rules). We discover a necessary condition called hyper-connectedness and a sufficient condition called Property ULLO for random LGE.  Our conditions are more general than earlier ones in the literature and are satisfied by several well-known preference domains. We also provide applications that can be covered uniquely by our results.