This paper by Roger B. Myerson and Mark A. Satterthwaite explores the design of efficient mechanisms for bilateral trading between a buyer and a seller, where both parties have unknown valuations for a single object. The authors characterize the set of allocation mechanisms that are Bayesian incentive compatible and individually rational, and show that ex post efficient mechanisms without outside subsidies are generally impossible. They provide methods to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker's expected profit. The paper also discusses the implications of these results in the context of public goods economies and the revelation principle, which states that any Bayesian equilibrium of a bargaining game can be equivalent to an incentive-compatible direct mechanism. The authors derive an impossibility result related to ex post efficiency and individual rationality, and present examples to illustrate their findings.This paper by Roger B. Myerson and Mark A. Satterthwaite explores the design of efficient mechanisms for bilateral trading between a buyer and a seller, where both parties have unknown valuations for a single object. The authors characterize the set of allocation mechanisms that are Bayesian incentive compatible and individually rational, and show that ex post efficient mechanisms without outside subsidies are generally impossible. They provide methods to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker's expected profit. The paper also discusses the implications of these results in the context of public goods economies and the revelation principle, which states that any Bayesian equilibrium of a bargaining game can be equivalent to an incentive-compatible direct mechanism. The authors derive an impossibility result related to ex post efficiency and individual rationality, and present examples to illustrate their findings.