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We study an exchange rule decomposability property requiring that if a fraction only of a recommended exchange takes place, then the remaining exchange be also recommended when including already exchanged quantities in individual endowments.We obtain justifications for the Walrasian exchange rule although this rule is not the only efficient, decomposable and equitable exchange rule.
Maniquet, F. (2000). On decomposable exchange rules. Economics Letters, 70(3), 375-380. https://hdl.handle.net/2078.5/208811 (Original work published 2001)