New variable-population paradoxes for resource allocation

We identify previously unnoticed ways in which agents can strategically distort allocation rules, by affecting the set of “active” agents. (i) An agent withdraws with his endowment. (ii) He gives control of his endowment to someone else and withdraws. (iii) He invites someone in and let him use some of his endowment. (iv) He pre-delivers to some other agent the net trade that the rule would assign to that second agent if that second agent had participated. In (i) and (ii), he and his co-conspirator may end up controlling resources that allow them to reach higher welfare levels than they otherwise would. In (iii) and (iv), he may end up with a bundle that he prefers to the one he would have been assigned had he not engaged in the manipulation. We show that (i) the Walrasian rule is not “withdrawing-proof”, nor “endowments-merging–proof, nor “endowments-splitting–proof”, but that it is “pre-delivery–proof”, and that (ii) canonical selections from the egalitarian-equivalence-in-trades solutions satisfy none of the properties.