Abstract:
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 show in private-value environments that any incentive compatible rule is implementable with small transfers. We obtain this permissive implementation result by proposing a natural extension of Abreu and Matsushima (1994) to incomplete information environments. Furthermore, in order to showcase the applicability of our results, we relate them to the recent developments in implementation theory. Next we revisit the conjecture by Abreu and Matsushima (1994), who claim that the extension of Abreu and Matsushima (1994) may be possible by mimicking the argument of Abreu and Matsushima (1992b). To the extent that our mechanism is a natural extension of that of Abreu and Matsushima (1994), we show by example that their conjecture is not unconditionally warranted to cover fully interdependent-value environments. We therefore identify a condition under which our results can be extended to interdependent-value environments and tightly connect this identified condition to the notion of strategic distinguishability due to Bergemann and Morris (2009b).