A Survey Of Implementation Theory Of Mechanism Design

Most traditional economic theories focus on the economic institutions that already exist and treat them as the given premise. Under this kind of guideline, economists are willing to explain and predict the economic and social outcomes that induced by these institutions. They often care about some given mechanism, such as competitive mechanism and monopolistic mechanism, and are interested in finding answers to these questions: what can kind of mechanism can guarantee the realization of Pareto optimal allocation? If so, then under what kind of environment and conditions will it be? On the contrary to these traditional questions in economic research, which are raised in a position of accepting the given mechanism, we can bring up another question: under a given environment, dose there exist a mechanism that can guarantee the realization of Pareto optimal allocation? This question is just the basic idea and starting point of mechanism design theory that was established by Leonid Hurwicz and developed by Roger B. Myerson, Eric S. Maskin and some other scholars who are also interested in this field. In mechanism design theory, not like the other traditional economic theories, the premise and starting point is not the existing mechanism, but the desired outcomes or social goals. What follows is that can we design an appropriate mechanism to accomplish these goals. If the answer is a positive one, then in what way dose this mechanism work? Just as Maskin said, the theory of mechanism design can be thought of as the"engineering"side of economic theory. Focuses on incentive and private information, the theory of mechanism design provides a framework for analyzing different institutions and allocation mechanism.In general, the main problem that mechanism design theory seeks to solve is that under the conditions of free choice, voluntary exchange and decentralized decision, for any desired goals that are pursued by a society, can and how can we design a mechanism to make the self-interest of agents that participate in the economic activities be consistent with the given goals of the society. In other words, while the agents maximizes there utility rationally, they also accomplish the desired goals of the designer. Further more, based on this question, mechanism design theory also discusses under what kind of constrictions will this mechanism exist and work properly. Mechanism design theory offers a very abstract and general framework that allows researchers to analyze all kinds of mechanisms systematically under assumptions that are not that strict. With this set of efficient tool, it is possible to compare different kind of economic mechanisms, to explore how the mechanism will affect the interactions between agents and the final allocation outcomes. Theoretically, we can use this framework provided by mechanism design theory to design and explore countless mechanisms of all kinds, in which market mechanism is only one particular case.Since Hurwicz (1960, 1972) constructed the framework that regarded mechanism as a information system in which agents interact and sent signals to a information center and introduced the concept of incentive compatibility that is so important in mechanism design theory, the field developed rapidly and widely. In 1970s, two important results in mechanism design theory were brought forward. One is the revelation principle, and the other is the framework of implementation. Myerson extended the revelation principle to the most general situation (1979, 1982, 1986), and also made some important contributions in the applications of the revelation principle. Although the revelation principle largely simplified the problem, it has an unavoidable flaw, the problem of multiple equilibria. Maskin (1999) was the first one to suggest a general solution. In fact, Maskin provided a complete framework to study the problem of implementation. Following his work, a lot of scholars worked on related issues and developed many important results that formed the subfield of'implementation theory'under mechanism design theory. Nowadays, implementation theory has already become the most important and active part of modern mechanism design theory.Except for the introduction, there are four chapters in this dissertation.The first chapter provided the basic structure of the implementation problem formally. By identifying the concept of environment, mechanism, social choice correspondence and so on, the foundational framework for the study was laid. Two important issues of implementation problem, information and equilibrium, were discussed. This chapter also listed some examples that are frequently used in the literature of implementation theory for further use. The implementation in dominant strategies was explored in the last part of the first chapter, where some characterization results were surveyed, including the famous Gibbard-Satterthwaite theorem.The second chapter discussed the implementation under conditions of complete information. The characterization results of Nash implementation was explored thoroughly, since these are the most important ones in the implementation theory and the foundation of almost all the other conclusions in refined Nash implementation, virtual implementation and Bayesian Nash implementation and so on. After that, the refined Nash implementation was explored. These fall into two classes: dominance-based refinements using simultaneous-move mechanisms, and sequential rationality refinements using sequential mechanisms. The former class includes subgame perfect implementation and the implementation by backward induction. The implementation in undominated Nash equilibrium is included in the other class. The last part of this chapter is about virtual implementation.The third chapter explored the implementation with incomplete information. This environment is the Bayesian environment that adopts the type representation to characterize the change of the environment. The characterization results of Bayesian Nash implementation was discussed first, as the arrangement in chapter 2, two classes of implementation using refinements of Bayesian equilibrium was then discussed, namely using undominated Bayesian equilibrium and sequential equilibrium. Virtual implementation with incomplete information was also explored.The last chapter discussed the criticism and challenges confront implementation theory, concluded the faultiness of the theory and pointed some possible direction of the future development of implementation theory. These problems that have either been ignored or studied in only the simplest settings included renegotiation of mechanisms, robustness of the mechanism, individual rationality, bounded rationality and implementation in dynamic environments.