AbstractThis paper develops a class of equilibrium-independent predictions of competitive equilibrium with indivisibilities. Specifically, we prove an analogue of the “Lone Wolf Theorem” of classical matching theory for the Baldwin and Klemperer (Econometrica 87(3):867–932, 2019) model of exchange economies with transferable utility, showing that any agent who does not participate in trade in some competitive equilibrium must receive her autarky payoff in every competitive equilibrium. Our results extend to approximate equilibria and to settings in which utility is only approximately transferable.