The interplay of interdependence and correlation in bilateral trade - KUNIMOTO, Takashi (Institutional Knowledge at Singapore Management University, 2024)
Cremer and McLean (1988) show that the seller can extract full surplus almost always by an incentive compatible, individually rational mechanism in a single-unit auction model with a ﬁnite type space in which agents’ beliefs are correlated and their valuations can be interdependent. We ﬁrst show that this paradoxically positive result can be extended to a model of bilateral trades. To make it more realistic, we investigate when ex-post eﬃciency and ex-post budget balance in bilateral trades can also be achieved by an incentive compatible, individually rational mechanism. We identify a necessary condition for the existence of such mechanisms and show that it is also suﬃcient for a two-type model. We next show that the identiﬁed condition is not suﬃcient in general. Through a series of examples, we show that the imposition of ex post budget balance in a bilateral trade model induces a delicate interaction between interdependent values and correlated beliefs, so that the existence of incentive compatible, individually rational mechanisms becomes a very subtle problem. Finally, focusing on a model with linear valuations, we give the precise sense in which a possibility result under interdependent values is more fragile than that under private values.