On decomposable exchange rules

We study an exchange rule decomposability property requiring that if a frac tion only of a recommended exchange takes place, then the remaining exchang e be also recommended when including already exchanged quantities in indivi dual endowments. We obtain justifications for the Walrasian exchange rule a lthough this rule is not the only efficient, decomposable and equitable exc hange rule. (C) 2001 Elsevier Science B.V. All rights reserved.