Essays in Dynamic Mechanism Design

Abstract

Questions of design in real economic situations are often dynamic. Managerial compensation, repeated auctions, and taxation are good examples. These demand the economic theory of mechanism design to be adept to changing underlying environments and evolving information. Adjusting existing static results to the dynamic models and introducing new ones is thus what the doctor orders. This collection of essays is a contribution to the theory and applications of dynamic mechanism design.

Chapter 1 asks the question: when can efficient institutions be made self enforcing? To answer it, the setting of bargaining with two sided asymmetric information is chosen-- a buyer has a hidden valuation for a good and a seller can produce the good at a hidden cost, both of which can change over time. The essay provides necessary and sufficient conditions for efficiency in this bilateral trading problem. In the process of establishing this result, a new notion of budget balance is introduced that allows the budget to be balanced dynamically, borrowing from the future but in a bounded fashion. Through a set of simple examples the comparative statics of the underlying economics forces of discounting and level of asymmetric information are explored.

In chapter 2, a dynamic and history dependent version of the payoff equivalence result is established. It provides an equivalence class of all mechanisms that are incentive compatible. Given two mechanisms that implement the same allocation, expected utility of an agent after any history in one must differ from the other through a history dependent constant. This result is then exploited to unify a host of existing results in efficient dynamic mechanism design. In particular a mechanism, and necessary and sufficient conditions are provided for the implementation of the efficient allocation in a general $N$-player dynamic mechanism design problem under participation constraints and budget balance.

Finally, in chapter 3 (coauthored with Marco Battaglini), we explore the applicability and limitations of the first-order approach in solving dynamic contracting models, and the nature of contracts when local constraints are not sufficient to characterize the optimum. A dynamic principal-agent model in which the agent's types are serially correlated forms the backbone of the analysis. It is shown that the first-order approach is violated in general environments; when the time horizon is long enough and serial correlation is sufficiently high, global incentive compatibility constraints generically bind. By fully characterizing a simple two period example, we uncover a number of interesting features of the optimal contract that cannot be observed in special environments in which the standard approach works. Finally, we show that even in complex environments, approximately optimal allocations can be easily characterized by focusing on a class of contracts in which the allocation is forced to be monotonic.