Essays on a Mechanism Design Approach to the Problem of Bilateral Trade and Public Good Provision

My dissertation consists of three chapters which contribute new theoretical results to the application of Myerson-Satterthwaite Theorem in mechanism design. Chapter 1 characterizes mechanisms satisfying Bayesian incentive compatibility (BIC) and interim individual rationality (IIR) in the classical public good provision problem. We propose a “stress test” for the results in the standard continuum type space by subjecting them to a finite type space. The main contribution of this paper is to propose a set of techniques that allow us to characterize the efficient and optimal mechanisms in a discrete setup. Using these techniques, we conclude that many of the known results gained within the standard continuum type space also hold when it is replaced by a discrete type space. Chapter 2 seeks for more positive results by employing two-stage mechanisms (Mezzetti (2004)), as efficient, voluntary bilateral trade is generally not incentive compatible in an interdependent-value environment (Fieseler, Kittsteiner, Moldovanu (2003) and Gresik (1991)). We propose Assumption 1 under which there exists a two-stage incentive compatible mechanism that achieves efficiency and voluntary participation. Third, within the same example, our Assumption 1 is satisfied if the seller’s degree of interdependence of preferences is not too high relative to the buyer’s counterpart. Finally, we show by the same example that if Assumption 1 is violated, our proposed two-stage mechanism violates voluntary trade. Chapter 3 clarifies how the interdependence in valuations and correlation of types across agents affect the possibility of efficient, voluntary bilateral trade in a model with discrete types, as efficient, voluntary bilateral trades are generally not incentive compatible in a private-value model with independently distributed continuous types (Myerson and Satterthwaite (1983)). First, we identify a necessary and sufficient condition for the existence of incentive compatible mechanisms inducing an efficient and voluntary trade in a two-type model. Using this result under linear valuations, we next conduct the comparative statics for how possibility results rely on the interdependence and correlation. Third, we extend our analysis to a general finite type space and propose a necessary condition for incentive compatible mechanisms inducing an efficient, voluntary trade.