Abstract. By definition, multilaterally strategy-proof mechanisms are immune to manipulation not only by individuals misrepresenting their preferences, but also by finite coalitions exchanging tradeable goods on the side. Continuum economies are defined in which both agents ’ identifiers and their privately known characteristics are joint i.i.d. random variables. For such economies, conditions are given for multilateral strategy-proofness to imply decentralization by a budget constraint with linear prices for tradeable goods and lump-sum transfers independent of individual characteristics. Also, adapting Aumann’s [1964a] key proof avoids using Lyapunov’s theorem or its corollary, Richter’s theorem on integrating a correspondence w.r.t. a non-atomic measure
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