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Leonid Hurwicz (1917-2008) was a major figure in modern theoretical economics whose contributions over 65 years spanned at least five areas: econometrics, nonlinear programming, decision theory, microeconomic theory, and mechanism design. While some of Hurwicz's work were published in journals, many remain scattered as chapters in books which are difficult to access and others were never published at all. 'The Collected Papers of Leonid Hurwicz' is the first volume in a series of four that will bring his oeuvre in one place, to bring to light the totality of his intellectual output, and to document his contribution to economics and the extent of his legacy, with the express purpose to make it easily available for future generations of researchers to build upon.

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

AbstractMany problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maximands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.