Allocation rules are very generally vulnerable to the strategic withholding of endowments

An allocation rule is “withholding-proof" if no agent ever benefits from withholding some of the resources they own, their final bundle consisting of what the rule assigns to them together with whatever they withheld. It was known that on the “classical" domain of continuous, monotone, and convex preferences, no rule is efficient and withholding-proof (Postlewaite, Rev Econ Stud 46:255–262, 1979). We show that this disappointing news persists under the simultaneous imposition of the following three restrictions: (i) the domain only consists of classical and homothetic preferences; (iii) when an agent withholds some of their endowment, they only recover a percentage of what they withhold, no matter how close to 0 that percentage is; (iii) rules are required to satisfy any of the central punctual requirements of fairness, the individual-endowments lower bounds, no-envy in trades (adapted from Tinbergen, Redelijke Inkomensverdeling, Second Edition. N.D. DeGulden Pers, Haarlem, 1953, and Foley, Yale Economic Essays 7:45–98, 1967) and egalitarian-equivalence in trades (adapted from Pazner and Schmeidler, Quart J Econ 92:671–687, 1978 and Schmeidler and Vind, Econometrica 40:637–642, 1972).