Essays on a mechanism design approach to the problem of bilateral trade and public good provision - ZHANG, Cuiling (Institutional Knowledge at Singapore Management University, 2020)
The dissertation consists of three chapters which studies a mechanism design approach to the problem of bilateral trade and public good provision. 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 subject- ing 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)). First, we show by means of a stylized example that the generalized two-stage Groves mechanism never guarantees voluntary trade, while it satisfies efficiency and in- centive compatibility. In a general environment, we next propose Condition α under which there exists a two-stage incentive compatible mechanism implementing an effi- cient, voluntary trade. Third, within the same example, we confirm that our Condition α is very weak because it holds as long as the buyer’s degree of interdependence of preferences is not too high relative to the seller’s counterpart. Finally, we show by the same example that if Condition α is violated, our proposed two-stage mechanism fails to achieve 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 compat- ible in a private-value model with independently distributed continuous types (Myerson and Satterthwaite (1983)). First, we identify a necessary condition for the existence of in- centive compatible mechanisms inducing an efficient and voluntary trade in a finite type model. Second, we show that the identified necessary condition becomes sufficient for a two-type model. Using this characterization in a model with linear valuations and two types, we next conduct the comparative statics for how possibility results rely on the inter- dependence and correlation. Third, using the linear programming approach, we establish the general existence of an efficient, incentive compatible trade in a model with two types. This suggests that voluntary trade becomes a stringent requirement in an interdependent values model with correlated signals.