The interplay of interdependence and correlation in bilateral trade

• Main Authors: KUNIMOTO, Takashi, ZHANG, Cuiling
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: auction theory; incentive compatible; individually rational mechanism; finite type space; correlated beliefs; interdependent valuations; bilateral trades; ex-post efficiency; budget balance; linear valuation; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2736; https://ink.library.smu.edu.sg/context/soe_research/article/3735/viewcontent/interdependence_and_correlation_March_30_2024.pdf
• Institution: Singapore Management University

Crémer 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.