Acknowledgements -- Introduction -- 1. Mechanisms and mechanism design -- 1.0. Introduction -- 1.1. Mechanisms and 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 -- 1.1. An Edgeworth box economy -- 1.6.2. The Walrasian goal function -- 1.6.3. Mechanisms : the competitive mechanism -- 1.6.4. Competitive equilibrium conditions -- 1.6.5. The competitive mechanism is a mechanism -- 1.6.6. The competitive mechanism illustrates some concepts used in mechanism design -- 1.6.7. Privacy preservation in the competitive mechanism -- 1.6.8. Deriving a mechanism (not the competitive mechanism) from a covering for the Walrasian goal function -- 1.6.9. Informational properties of the two mechanisms -- 1.6.10. The rectangles methods applied to the Walrasian goal function -- informal -- 1.7. Introductory discussion of informational efficiency concepts -- 1.8. A national forest. 2. From goals to means : constructing mechanisms -- 2.1. Phase one : mechanism construction -- 2.1.1. Two examples -- 2.1.2. Constructing a "universal" method of designing informationally efficient mechanisms realizing a given goal function -- 2.1.3. The method of rectangles (RM) -- 2.2. Phase 2 : constructing decentralized mechanisms, from parameter indexed product structures : transistion to message-indexed product structures -- 2.2.0. Introduction -- 2.2.1. Basic concepts -- 2.2.2. The L-dot example -- 2.2.3. More examples -- 2.2.4. General issues in mechanism construction -- 2.2.5. Mechanism construction for partitions -- 2.3. Smooth transversal construction for partitions by the "Flagpole" method -- 2.3.1. Flagpoles : general principles -- 2.3.2. Flagpoles : example 2 (augmented inner product) -- 2.3.3. Flagpoles : a Walrasian example -- 2.3.4. Unique solvability implies partition -- 2.4. Analytic aspects -- 2.4.1. Phase two via condensation. General principles -- 2.4.2. The Mount-Reiter condensation theorem (sufficiency) -- 2.4.3. Walrasian mechanism construction -- 2.4.4. Phase two of mechanism design via condensation for the augmented two-dimensional inner product -- 2.5. Overlaps -- 2.5.0. Constructing a mechanism when the parameter-indexed product structure is not a partition : an example -- Appendix. 2.6. Informational efficiency -- 2.6.1. Main results -- 2.6.2. The maximality of reflexive RM-coverings -- 2.6.3. Informational efficiency : general considerations -- 2.6.4. A comment on informational efficiency concepts -- 2.6.5. Minimal informational size is achievable by an rRM mechanism -- 2.6.6. Two rRM coverings of different informational size for the same goal function: an example -- Appendix -- 3. Designing informationally efficient mechanisms using the language of sets -- 3.1. Introduction -- 3.2. Mechanism design -- 3.2.1. Decentralization -- 3.3. Mechanisms and coverings -- 3.4. A systematic process for constructing an rRM covering -- 3.4.1. OrRM: an algorithm for constructing an rRM covering of a finite parameter space that is minimal in the class of rectangular, F-contour contained coverings -- 3.5. Constructing a mechanism from a covering by the transversals method (TM) -- g 3.6. Coverings and partitions -- 3.7. Informational efficiency -- 3.7.1. Introduction -- 3.7.2. Observational efficiency -- 3.7.3. The maximality of rRM-coverings -- 3.7.4. Informational size and coarseness -- 3.8. Section 1.8 revisited : a graphical presentation -- 3.9. Strategic behavior -- 3.9.1. Dominant strategy implementation -- 3.9.2. Designing informationally efficient Nash-implementing mechanisms -- Appendix : Characterizations of partitions. 4. Revelation mechanisms -- 4.1. Introduction -- 4.1.1. computational complexity of functions -- 4.1.2. Separator sets and quotients -- 4.1.3. Algebraic conditions -- 4.1.4. Privacy-preserving mechanisms -- 4.2. Initia set-theoretic constructions -- 4.2.1. Encoded and essential revelation mechanisms -- 4.2.2. F-equivalence and encoded revelation mechanisms -- 4.3. The topological case -- 4.3.1. Differential separability -- 4.3.2. The number of variables on which F really depends -- 4.3.3. Rank conditions and construction of an essential revelation mechanism for F -- 4.4. Proofs and examples -- 4.4.1. Leontief and Abelson theorem -- 4.4.2. Leontief's theorem -- 4.4.3. An example of the coordinate construction -- 4.4.4. Proof of theorem 4.4.6 -- References -- Index.