On the equivalence of bayesian and dominant strategy implementation’, Econometrica 81(1

We study the equivalence between Bayes-Nash Incentive Compat-ibility (BIC) and Dominant Strategy Incentive Compatibility (DIC) in a standard social choice environment with linear utility and one-dimensional types. We consider two notions of equivalence: one based on agentsinterim utilities (U-equivalence), and a stronger one based on conditional expected probabilities of choosing each alternative (P-equivalence). Our main results are: 1) For any BIC mechanism there is a P-equivalent DIC mechanism in settings with two social alterna-tives. 2) We construct a symmetric, BIC mechanism for which there is no P-equivalent DIC mechanism in an example with three alterna-tives. 3) In general settings, for any symmetric BIC mechanism there exists a symmetric, DIC and U-equivalent mechanism. Our insights are based on elegant mathematical results about the existence of monotone measures with given monotone marginals. We wish to thank Sergiu Hart, Philippe Jehiel and Ennio Stacchetti for very helpful discussions. We have also bene\u85ted from excellent comments made by a co-editor and three anonymous referees. Moldovanu wishes to thank the German Science Foundation and the European Research Council for \u85nancial support, and Shi thanks the \u85nancia