{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T19:15:18Z","timestamp":1788462918663,"version":"build-2803163510"},"reference-count":42,"publisher":"The Econometric Society","issue":"4","funder":[{"DOI":"10.13039\/501100001352","name":"National University of Singapore","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001352","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.<\/jats:p>","DOI":"10.3982\/ecta14698","type":"journal-article","created":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T01:04:27Z","timestamp":1563930267000},"page":"1367-1390","source":"Crossref","is-referenced-by-count":16,"title":["Equivalence of Stochastic and Deterministic Mechanisms"],"prefix":"10.3982","volume":"87","author":[{"given":"Yi-Chun","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Economics, Risk Management Institute, National University of Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"He","sequence":"additional","affiliation":[{"name":"Department of Economics, Chinese University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangtao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics, Singapore Management University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yeneng","family":"Sun","sequence":"additional","affiliation":[{"name":"Departments of Economics and of Mathematics, Risk Management Institute, National University of Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2019]]},"reference":[{"issue":"1","key":"ecta200041-bib-0001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.geb.2010.07.007","volume":"72","author":"Aggarwal","year":"2011","journal-title":"Games and Economic Behavior"},{"issue":"3","key":"ecta200041-bib-0002","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1070\/RM1972v027n03ABEH001378","volume":"27","author":"Arkin","year":"1972","journal-title":"Russian Mathematical Surveys"},{"issue":"4","key":"ecta200041-bib-0003","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1111\/1468-0262.00231","volume":"69","author":"Bester","year":"2001","journal-title":"Econometrica"},{"key":"ecta200041-bib-0004","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-34514-5","volume-title":"Measure Theory","volume":"II","author":"Bogachev","year":"2007"},{"issue":"4","key":"ecta200041-bib-0005","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.2307\/2938181","volume":"59","author":"Border","year":"1991","journal-title":"Econometrica"},{"issue":"3","key":"ecta200041-bib-0006","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00199-008-0347-7","volume":"39","author":"B\u00f6rgers","year":"2009","journal-title":"Economic Theory"},{"key":"ecta200041-bib-0007","unstructured":"Cai, Y., C. 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