Mechanism design is the field of economics that treats institutions and procedures as variables that can be selected in order to achieve desired objectives. An important aspect of a mechanism is the communication among its participants that it requires, which complements other design features such as incentives and complexity. A calculus-based theory of communication in mechanisms is developed in this book. The value of a calculus-based approach lies in its familiarity as well as the insight into mechanisms that it provides. Results are developed concerning (i) a first order approach to the construction of mechanisms, (ii) the range of mechanisms that can be used to achieve a given objective, as well as (iii) lower bounds on the required communication.

“Communication in Mechanism Design by Steve Williams is a contribution of major importance. This applies both to the role in advancing the topic of mechanism design for economic theorists as well as to the mathematical exposition which is accessible without compromising on content. The reformulation of the Frobenius Theorem, in a form suitable for applications in mechanism design, is Williams’ own and provides a crucial step forward. In his preface, Steve Williams says “This text complements Hurwicz and Reiter”. Steve is much too modest in his comment. In fact, his version of the Frobenius Theorem is a natural and brilliant solution to a difficult problem.”
- Leonid Hurwicz, Nobel Laureate, University of Minnesota

In his very interesting book, Steve Williams provides an important and deep fundamental analysis of the structure and role of information in mechanisms. This is a must read for anyone interested in the foundations of mechanism design.- John Ledyard, California Institute of Technology

"This book explores in detail the use of calculus on manifolds to design decentralized mechanisms whose performance achieves specified economic objectives. The writing makes the uses of calculus on manifolds accessible to a reader familiar with standard multi-variable calculus. The book makes a fine a companion volume to Hurwicz and Reiter's Designing Economic Mechanisms. It should appeal to mathematicians as well as economists."
-Stanley Reiter, Northwestern University

"This book is a valuable addition to economics and the mechanism design literature. Williams has nicely resurrected, clarified, illustrated, and described an important part of this area that has not been as fully exploited as it could and should."
Donald Saari, University of California, Irvine