Implementation with transfers - CHEN, Yi-Chun (Institutional Knowledge at Singapore Management University, 2016)
We say that a social choice rule is implementable with (small) transfers if one candesign a mechanism whose set of equilibrium outcomes coincides with that speciÖed bythe rule but the mechanism allows for (small) ex post transfers among the players. Weshow in private-value environments that any incentive compatible rule is implementablewith small transfers. We obtain this permissive implementation result by proposinga natural extension of Abreu and Matsushima (1994) to incomplete information environments.Furthermore, in order to showcase the applicability of our results, we relatethem to the recent developments in implementation theory. Next we revisit the conjectureby Abreu and Matsushima (1994), who claim that the extension of Abreu andMatsushima (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 ofAbreu and Matsushima (1994), we show by example that their conjecture is not unconditionallywarranted to cover fully interdependent-value environments. We thereforeidentify a condition under which our results can be extended to interdependent-valueenvironments and tightly connect this identiÖed condition to the notion of strategicdistinguishability due to Bergemann and Morris (2009b).