Herbert Scarf

Herbert Scarf
Naissance	25 juillet 1930 Philadelphie ( États-Unis)
Nationalité	américaine
Champs	Économie (synthèse néo-classique)
Institution	Université Yale,
Diplômé de	Université Yale
Renommé pour	les algorithmes de calcul de l’équilibre général
Distinctions	membre de l’Académie américaine des Arts et des Sciences
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Après avoir obtenu en 1954 son Ph.D à l’Université Yale, Herbert Scarf débute sa carrière scientifique à la Rand Corporation. En 1957, il est nommé professeur au département de statistique de l’Université Stanford en Californie. Depuis 1963 il est professeur à la Cowles Foundation de l’Université Yale. En 1963, Herbert Scarf et Gérard Debreu montrent la convergence du noyau d’un jeu coopératif (jeu) vers l’équilibre général. Dans la théorie des jeux coopératifs, le noyau est une allocation des ressources disponibles telle qu’aucune coalition de consommateurs ne peut trouver une autre allocation qui soit meilleure pour tous ses membres. On commence avec deux consommateurs et ensuite on réplique plusieurs fois cette économie. Herbert Scarf est surtout connu pour ses recherches consacrées au calcul de l’équilibre général. Il a proposé un algorithme qui permet de calculer le point fixe d’une application. En utilisant cet algorithme il est possible de trouver l’équilibre général pour des modèles avec des dizaines d’équations. Scarf a aussi donné des exemples où le mécanisme du tâtonnement imaginé par Léon Walras ne conduit pas à l’équilibre.

Références

Son livre le plus fameux est “The Computation of Economic Equilibria”, Yale University Press, 1973

Parmi ses nombreux articles, on peut citer:

• "On Differential Games with Survival Payoff", 1957, Annals of Mathematical Statistics.
• "Games with Partial Information", with L.S.Shapley, 1957, in Annals of Mathematical Statistics.
• Studies in the Mathematical Theory of Inventory and Production with K.J. Arrow and S. Karlin, 1958
• "The Optimality of (S, s) Policies in the Dynamic Inventory Problem." 1959, in Mathematical Methods in the Social Sciences
• "Some Examples of Global Instability of the Competitive Equilibrium", 1960, IER.
• "Optimal Policies for a Multi-echelon Inventory Problem," with A. J. Clark, 1960, Management Science
• "Approximate Solutions to a Simple Multi-Echelon Inventory Problem" with A.J. Clark, 1962, in Arrow et al, editors, Studies in Applied Probability and Management Science
• "An Analysis of Markets with a Large Number of Participants", 1962, Recent Advances in Game Theory.
• "A Survey of Analytic Techniques in Inventory Theory." 1963, in Scarf et al, editors, Multistage Inventory Models and Techniques
• "A Limit Theorem on the Core of an Economy", with G. Debreu, 1963, Econometrica.
• "The Approximation of Fixed Points of a Continuous Mapping," 1967, SIAM
• "On the Computation of Equilibrium Prices", 1967 in Ten Economic Studies in the Tradition of Irving Fisher.
• "The Core of an N-Person Game", 1967, Econometrica.
• "An Example of an Algorithm for Calculating General Equilibrium Prices," 1969, AER
• "On the Existence of a Cooperative Solution for a General Class of N-Person Games", 1971, JET.
• "The Limit of the Core of an Economy" with G. Debreu, 1972, in McGuire and Radner, editors, Decision and Organization
• The Computation of Economic Equilibrium (with collaboration of T. Hansen), 1973.
• "On Cores and Indivisibility", with L.S. Shapley, 1974, JMathE.
• "The Solution of Systems of Piecewise Linear Equations," with B. C. Eaves, 1976, Mathematics of Operations Research
• "An Observation on the Structure of Production Sets with Indivisibilities," 1977, PNAS
• "Production Sets with Indivisibilities, Part I: Generalities: & Part II: The Case of Two Activities", 1981, Econometrica
• The Computation of Equilibrium Prices" 1982, in Arrow and Intriligator, editors, Handbook of Mathematical Economics, Volume II
• "Fixed Point Theorems and Economic Analysis,", 1983, American Scientist
• "The Computation of Equlibrium Prices", 1984, in Scarf and Shoven, editors, Applied General Equilibrium Analysis.
• "Integral Polyhedra in Three Space," 1985, Mathematics of Operations Research
• "Neighborhood Systems for Production Sets with Indivisibilities," 1986, Econometrica
• Testing for Optimality in the Absence of Convexity", 1986, in Heller, Starr and Starrett, editors, Social Choice and Public Decision Making.
• "Notes on the Core of a Productive Economy.", 1986, in Hildenbrand and Mas-Colell, editors, Contributions to Mathematical Economics
• "A Theorem in Search of a Simple Proof." 1989, in Anderson et al, editors, Probability, Statistics, and Mathematics,
• "Mathematical Programming and Economic Theory," 1990, Operations Research
• "The Origins of Fixed Point Methods." 1991, in Lenstra et al., editors, History of Mathematical Programming
• "The Generalized Basis Reduction Algorithm," with L. Lovász, 1992, Mathematics of Operations Research
• "The Frobenius Problem and Maximal Lattice Free Bodies" with D.F. Shallcross, 1993, Mathematics of Operations Research
• "Shortest Integer Vectors," with D.F. Shallcross, 1993, Mathematics of Operations Research
• "The Allocation of Resources in the Presence of Indivisibilities," 1994, JEP
• "The Complex of Maximal Lattice Free Simplices," with I. Bárány and R. Howe, 1994, Mathematical Programming
• "Tjalling Charles Koopmans, 1910-1985 Biographical Memoir," 1995, at NAS (pdf file)