Implementation with Transfers

We say that a social choice rule is implementable with (small) transfers if one can design a mechanism whose set of equilibrium outcomes coincides with that specified by the rule but the mechanism allows for (small) ex post transfers among the players. We then show in private-value environments that any incentive compatible rule is implementable with small transfers. Therefore, our mechanism only needs small ex post transfers to make our implementation results completely free from the multiple equilibrium problem. In addition, our mechanism possesses the unique equilibrium that is robust to higher-order belief perturbations. We also identify a class of interdependent-value environments to which our results can be extended.