A mechanism is a mathematical structure that models institutions through which economic activity is guided and coordinated. There are many such institutions; markets are the most familiar ones. Lawmakers, administrators and officers of private companies create institutions in order to achieve desired goals. They seek to do so in ways that economize on the resources needed to operate the institutions, and that provide incentives that induce the required behaviors. This book presents systematic procedures for designing mechanisms that achieve specified performance, and economize on the resources required to operate the mechanism. The systematic design procedures are algorithms for designing informationally efficient mechanisms. Most of the book deals with these procedures of design. When there are finitely many environments to be dealt with, and there is a Nash-implementing mechanism, our algorithms can be used to make that mechanism into an informationally efficient one. Informationally efficient dominant strategy implementation is also studied.
1. Mechanisms and mechanism design; 1.1. Introduction to mechanisms and mechanism design; 1.2. Environments and goal functions; 1.3. Mechanisms: message exchange processes and game forms; 1.4. Initial dispersion of information and privacy preservation; 1.5. Mechanism design; 1.6. Mechanism design illustrated in a Walrasian example; 1.7. The rectangles method applied to the Walrasian goal function-informal; 1.8. Introductory discussion of informational efficiency concepts; 1.9. Regulation of logging in a national forest - an example of mechanism design; 2. From goals to means: constructing mechanisms; 2.1. Mechanism construction: Phase One; 2.2. Phase Two: constructing decentralized; 2.3.1. Flagpoles-Principles; 2.4.1. Phase Two via condensation: Principles; 2.5. Overlaps; 2.6.1. Main results; 3. Designing informationally efficient mechanisms using the language of sets; 3.1. Introduction; 3.2. Mechanism design; 3.3. Mechanisms and coverings; 3.4. A systematic process (an algorithm) for constructing and RRM covering; 3.5. Transversals; 3.6. Coverings and partitions; 3.7. Informational efficiency; 3.8. Example 1.9 revisited - a graphical presentation; 3.9. Informationally efficient mechanisms with strategic behavior; 4. Revelation mechanisms (coauthored with Kenneth R. Mount); 4.1. Introduction; 4.2. Initial set theoretic constructions; 4.3. The topological case; 4.4. Proofs and examples.
