One of the central questions of economics relates to the coordination of individual units within a large organization to achieve the central objectives of that organization. This book examines the problems involved in allocating resources in an economic system where decision-making is decentralized into the hands of individuals and individual enterprises. The decisions made by these economic agents must be coordinated because the input decisions of some must eventually equal the output decisions of others. Coordination arises naturally out of the mathematical theory of optimization but there is still the question of how it can be achieved in practice with dispersed knowledge. The essays here explore the many facets of this problem. Nine papers are grouped under the title 'Economies with a single maximand'. They include papers on static and dynamic optimization, decentralization within firms, and nonconvexities in optimizing problems. Fourteen papers are concerned with 'Economies with multiple objectives'. Among the topics covered here are stability of competitive equilibrium, stability in oligopology, and dynamic shortages. The final part of the book includes three papers on informational efficiency and informationally decentralized systems. Leonid Hurwitcz is the Nobel Prize Winner 2007 for The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, along with colleagues Eric Maskin and Roger Myerson, for his work on the effectiveness of markets.

### Contents

Preface; Acknowledgments for reprinted articles; Part I. General Introduction: the design of resource allocation mechanisms L. Hurwicz; Part II. Economies with a Single Maximand: 1. General survey: decentralization and computation in resource allocation K. J. Arrow and L. Hurwicz; 2. Static characterization: constraint qualifications in maximization problems K. J. Arrow, L. Hurwicz and H. Uzawa; Static characterization: quasi-concave programming K. J. Arrow and A. C. Enthoven; 3. Decentralization within firms: optimization, decentralization, and internal pricing in business firms K. J. Arrow; 4. Dynamic characterization: gradient methods for constrained maxima K. J. Arrow and L. Hurwicz; 5. The handling of nonconvexities: reduction of constrained maxima to saddle-point problems K. J. Arrow and L. Hurwicz; The handling of nonconvexities: a general saddle-point result for constrained optimization K. J. Arrow, F. J. Gould and S. M. Howe; The handling of nonconvexities: convexity of asymptotic average production possibility sets L. Hurwicz and H. Uzawa; Part III. Economies with Multiple Objectives: 6. Stability of competitive equilibrium: on the stability of competitive equilibrium I K. J. Arrow and L. Hurwicz; Stability of competitive equilibrium: on the stability of competitive equilibrium II K. J. Arrow, H. D. Block and L. Hurwicz; Stability of competitive equilibrium: on the stability of competitive equilibrium II: postscript K. J. Arrow and L. Hurwicz; Stability of competitive equilibrium: some remarks on the equilibria of economic systems K. J. Arrow and L. Hurwicz; 7. Competitive stability under weak gross substitutability: the 'Euclidean distance' approach K. J. Arrow and L. Hurwicz; Competitive stability under weak gross substitutability: nonlinear price adjustment and adaptive expectations K. J. Arrow and L. Hurwicz; 8. Stability in oligopoly: stability of the gradient process in n-person games K. J. Arrow and L. Hurwicz; 9. Studies in local stability: a theorem on expectations and the stability of equilibrium A. C. Enthoven and K. J. Arrow; Studies in local stability: a note on expectations and stability K. J. Arrow and M. Nerlove; Studies in local stability: a note on dynamic stability K. J. Arrow and M. McManus; Studies in local stability: stability independent of adjustment speed K. J. Arrow; 10. Dynamic shortages: dynamic shortages and price rises: the engineer-scientist case K. J. Arrow and W. M. Capron; Dynamic shortages: price-quantity adjustments in multiple markets with rising demands K. J. Arrow; 11. Foundations of price dynamics: toward a theory of price adjustment K. J. Arrow; Part IV. General Characterizations of Allocation Processes: Optimality and information efficiency in resource allocation processes L. Hurwicz; On the dimensional requirements of informationally decentralized Pareto-satisfactory processes L. Hurwicz; On informationally decentralized systems L. Hurwicz; Appendix: an optimality criterion for decision-making under ignorance K. J. Arrow and L. Hurwicz; Author index; Subject index; Index of examples.