On the manipulability of allocation rules through endowment augmentation

We formulate and study the requirement on an allocation rule that no agent should be able to benefit by artificially augmenting their endowment. This can be either through simply exaggeration or through a transfer of resources from outside of the current trading partners, resources that have to be returned after the rule is applied and the agent has received their assignment. We show that the Walrasian rule is not “augmentation-proof” even on standard domains. More seriously, no efficient selection from the individual-endowments lower bounds correspondence, or from the no-envy correspondence, or from the egalitarian-equivalent correspondence is augmentation-proof. These impossibilities hold even when preferences are homothetic, and even if the agent cannot augment their endowment by more than an arbitrarily small proportion of the resources they truly own.