PUBLICATIONS

"Group Invariant Integration and the Fundamental Theorem of Algebra." In Proceedings, National Academy of Sciences, May, 1952.

"Shaped Sources for Teletherapy Units" (with W. Pollard), Nucleonics, February, 1953.

"Games with Partial Information" (with L. Shapley). In Volume III, Contributions to the Theory of Games, eds. M. Dresher, A.W. Tucker and P. Wolfe, in the series Annals of Mathematical Studies, eds. E. Artin and M. Morse. Princeton University Press, 1957, pp. 213-229.

"On Differential Games with Survival Payoffs." In Volume III, Contributions to the Theory of Games, eds. M. Dresher, A.W. Tucker and P. Wolfe, in the series Annals of Mathematical Studies, eds. E. Artin and M. Morse. Princeton University Press, 1957, pp. 393-405.

"The Nature and Structure of Inventory Problems" (with K.J. Arrow and S. Karlin); "Summaries," (with K.J. Arrow and S. Karlin); "Inventory Models of the Arrow-Harris-Marschak Type with Time Lag" (with S. Karlin); "A Min-Max Solution of an Inventory Problem," "Stationary Operating Characteristics of an Inventory Model with Time Lag," and "Inventory Models and Related Stochastic Processes" (with S. Karlin). In Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow, S. Karlin and H.E. Scarf. Stanford University Press, 1958.

"A Dynamic Theory of Consumers' Preferences," Technical Report No. 10, Statistics Department, Stanford University, March 25, 1959

"Bayes Solutions of the Statistical Inventory Problem," Annals of Mathematical Statistics, (1959), 30(2): 490-508.

"Some Examples of Global Instability of the Competitive Equilibrium," International Economic Review, Vol. l, 1960.

"The Optimality of (S, s) Policies in the Dynamic Inventory Problem." In Mathematical Methods in the Social Sciences 1959. Proceedings of the First Stanford Symposium. Stanford University Press, 1959. Also in Optimal Pricing, Inflation, and the Cost of Price Adjustment, eds., E. Sheshinski and Y. Weiss. Cambridge, MA: MIT Press, 1993.

"Optimal Policies for a Multi-echelon Inventory Problem" (with A.J. Clark), Management Science, Vol. 6, No. 4, 1960. (This paper has been designated as one of the ten most influential papers published in the first fifty years of the journal.)

"Some Remarks on Bayes Solutions to the Inventory Problem," Naval Research Logistics Quarterly (December 1960), 7(4): 591-596

"Approximate Solutions to a Simple Multi-Echelon Inventory Problem" (with A.J. Clark). In Studies in Applied Probability and Management Science, eds. K.J. Arrow, S. Karlin, and H. E. Scarf. Stanford University Press, 1962.

"An Analysis of Markets with a Large Number of Participants." Princeton University Conference Paper. In Recent Advances in Game Theory. Philadelphia: The Ivy Curtis Press, 1962.

"A Survey of Analytic Techniques in Inventory Theory." In Multistage Inventory Models and Techniques, eds. H.E. Scarf, D. M. Gilford and M. W. Shelley. Stanford University Press, 1963.

"A Limit Theorem on the Core of an Economy" (with G. Debreu), International Economic Review, Vol. 4, No. 3, 1963. Reprinted in Classics in Game Theory, ed. H. Kuhn. Princeton University Press, 1997. Reprinted in Economic Games, Bargaining and Solutions, ed. O.F. Hamouda and J.C.R. Rowley, Foundations of Probability, Econometrics and Economic Games Series, series no. 3, Edward Elgar Publishing, 1997. [CFP 200]

"An Elementary Proof of a Theorem on the Core of an N Person Game," Cowles Foundation Preliminary Paper 50426

"An Algorithm for a Class of Nonconvex Programming Problems," Cowles Foundation Discussion Paper 211, July, 1966. [25pp]

"The Core of an N-Person Game," Econometrica, Vol. 35, No. 1, 1967. Reprinted in Classics in Game Theory, ed. H. Kuhn. Princeton University Press, 1997. Reprinted in Economic Games, Bargaining and Solutions, ed. O.F. Hamouda and J.C. R. Rowley, Foundations of Probability Econometrics and Economic Games Series, series no. 3, Edward Elgar Publishing, 1997. [CFP 277]

"The Approximation of Fixed Points of a Continuous Mapping," SIAM Journal of Applied Mathematics, Vol.15, No. 5, 1967. [CFP 262]

"On the Computation of Equilibrium Prices." In Ten Economic Studies in the Tradition of Irving Fisher. New York: John Wiley & Sons, 1967. [CFP 271]

"On the Existence of Cooperative Solutions to a Class of N-Person Games." In Indirect Measurement of Utility, U.S. Arms Control and Disarmament Agency (ACDA), November 1968. Also in Game-Theoretic Models of Cooperation & Conflict, eds. J.P. Mayberry, et al. Underground Classics in Economics Series. Boulder, CO: Westview Press, 1992.

"An Example of an Algorithm for Calculating General Equilibrium Prices," The American Economic Review, Vol. 59, No. 4, 1969. [CFP 308]

"On the Application of a Recent Combinatorial Algorithm" (with T. Hansen), Cowles Foundation Discussion Paper No. 272, April, 1969

"On the Existence of a Cooperative Solution for a General Class of N-Person Games," Journal of Economic Theory, Vol. 3, No. 2, 1971. [CFP 358]

"The Limit of the Core of an Economy" (with G. Debreu). In Decision and Organization, Amsterdam: North-Holland, 1972. [CFP 369]

The Computation of Economic Equilibria (with collaboration of T. Hansen), Cowles Foundation Monograph No. 24. New Haven: Yale University Press, 1973.

"On Cores and Indivisibility" (with L. Shapley), Journal of Mathematical Economics, Vol. 1, No. 1, 1974. Also in Studies in Mathematics, eds. G.B. Dantzig and B.C. Eaves. The Mathematical Association of America, Vol. 10, 1974.

"The 1975 Nobel Prize in Economics: Resource Allocation," Science Magazine, Vol. 190, November, 1975.

"The Solution of Systems of Piecewise Linear Equations" (with B. C. Eaves), Mathematics of Operations Research (1976), 1(1). [CFP 434]

"An Observation on the Structure of Production Sets with Indivisibilities," Proceedings, National Academy of Sciences (1977), 74(9): 1-27 [CFP 454]

"Production Sets with Indivisibilities, Part I: Generalities," Econometrica (January 1981), 49(1): 1-32. [CFP 516]

"Production Sets with Indivisibilities, Part II: The Case of Two Activities," Econometrica (March 1981), 49(2): 395-423. [CFP 522]

"Comment on: 'On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example,'" International Economic Review (1981), 22(2): 469-470.

"The Computation of Equilibrium Prices: An Exposition." In Handbook of Mathematical Economics, Volume II, eds. K. Arrow and Alan Kirman, chapter 4, 1982. [CFP 541]

"Fixed Point Theorems and Economic Analysis," American Scientist (May 1983),71(3): 289-296.

Applied General Equilibrium Analysis, eds. H.E. Scarf and J. Shoven. Cambridge University Press, 1984.

"Integral Polyhedra in Three Space," Mathematics of Operations Research (August 1985), 10(3): 403-438. [CFP 624a]

"Neighborhood Systems for Production Sets with Indivisibilities," Econometrica, Vol. 54, No. 3, 1986. [CFP 648]

"Testing for Optimality in the Absence of Convexity." In Social Choice and Public Decision Making: Essays in Honor of Kenneth J. Arrow, Volume 1, eds. W. Heller, R. Starr and D. Starrett. Cambridge University Press, 1986. [CFP 655]

"Notes on the Core of a Productive Economy." In Contributions to Mathematical Economics (in Honor of Gerard Debreu), eds. W. Hildenbrand and A. Mas-Colell. Amsterdam: North-Holland, 1986. [CFP 646]

"A Theorem in Search of a Simple Proof." In Probability, Statistics, and Mathematics, Papers in Honor of Samuel Karlin, eds. T.W. Anderson, K.B. Athreya, and D.L. Iglehart. Academic Press, Inc., 1989.

"Computation of General Equilibrium." In General Equilibrium, eds. John Eatwell, Murray Milgate, Peter Newman, The New Palgrave: A Dictionary of Economics, London: The Macmillan Press Ltd, 1989, pp. 84-97.

"The Shapes of Polyhedra" (with R. Kannan and L. Lovász), Mathematics of Operations Research, Vol. 15, No. 2, 1990. [CFP 753]

"Mathematical Programming and Economic Theory," Operations Research, Vol. 38, No. 3, 1990. [CFP 763]

"Economic Equilibrium and Soviet Economic Reform," Cowles Foundation Discussion Paper, No. 969, February, 1991.

"The Origins of Fixed Point Methods." In History of Mathematical Programming, A Collection of Personal Reminiscences, eds. J.K. Lenstra, A.H.G. Rinnooy Kan and A. Schrijver. Amsterdam: North-Holland, 1991, pp. 126-134.

"The Generalized Basis Reduction Algorithm" (with L. Lovász), Mathematics of Operations Research, Vol. 17, No. 3, 1992. [CFP 818]

"Tjalling Charles Koopmans (August 28, 1910-February 26, 1985)." In Biographical Memoirs, Volume 67, pp. 263-291. National Academy Press, 1995. [CFDP 1029]

"An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming" (with W. Cook, T. Rutherford, and D.F. Shallcross), ORSA Journal on Computing, Vol. 5, No. 2, 1993. [CFP 906]

"The Frobenius Problem and Maximal Lattice Free Bodies" (with D.F. Shallcross), Mathematics of Operations Research, Vol. 18, No. 3, 1993. [CFP 892]

"Shortest Integer Vectors" (with D.F. Shallcross), Mathematics of Operations Research (1993), 18(3): 517-522. [CFP 848]

"The Complex of Maximal Lattice Free Simplices" (with I. Bárány and R. Howe), Mathematical Programming, Vol. 66, No. 3, 1994. [CFP 888]

"The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, Vol. 8, No. 4, 1994. Reprinted in Readings in Microeconomic Theory, ed. Manfredi M.A. LaManna The Dryden Press, Harcourt Brace & Company, 1997. [CFP 880]

Foreword to Applied General Equilibrium and Economic Development, edited by J. Mercenier and T.N. Srinivasan. Ann Arbor: The University of Michigan Press, 1994.

"Matrices with Identical Sets of Neighbors" (with I. Bárány), Cowles Foundation Discussion Paper No. 1127, May 1996. Mathematics of Operations Research. Vol. 23, No. 4, 1998. [CFP 973]

"Test Sets for Integer Programs," Mathematical Programming, Vol. 79, 1997, pp. 355-368. [CFP 954]

"The Topological Structure of Maximal Lattice Free Convex Bodies: The General Case" (with I. Bárány and D. Shallcross), Mathematical Programming, Vol. 80, No.1, January 1998, pp. 1-15. [CFP 959]

"Optimal Inventory Policies When Sales are Discretionary," International Journal of Production Economics, Vols. 93-94, January 2005, pp. 111-119 [CFP 1104]

"How to Compute Equilibrium Prices in 1891" (with William C. Brainard), American Journal of Economics and Sociology (January 2005), 64(1): 57-83 [CFDP 1272].

"Inventory Theory," Operations Research, Vol. 50, No. 1, 2002, pp. 186-191. [CFP 1036]

"Uniqueness of Equilibrium in the Multi-Country Ricardo Model." In Timothy J. Kehoe, T.N. Srinivasan and John Whalley, eds., Frontiers in Applied General Equilibrium Modeling: In Honor of Herbert Scarf, Cambridge University Press, 2005, pp. 24-43 (with C.A. Wilson) [CFDP 1431, July 2003].

"Neighborhood Complexes and Generating Functions for Affine Semigroups." Discrete Computational Geometry 35: 385-403 (with K.M. Woods).

"Two New Proofs of Afriat's Theorem" (with A. Fostel, M.J. Todd), Economic Theory, Vol. 24, pp. 211-219, 2004. [CFP 1145]

Comments on "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science (December 2004), 50(12): 1791-1793.

"The Structure of the Complex of Maximal Lattice Free Bodies for a Matrix of Size (n + 1) x n," in Grotschel et al., Building Bridges between Mathematics and Computer Science, BSMS, Vol. 19, ISBN: 978-3-540-85218-6). [http://www.springer.com/math/numbers/book/978-3-540-85218-6]

"The Computation of Equilibria for the Walrasian Model: A Personal Account." In Pascal Bridel, ed., General Equilibrium Analysis: A Century after Walras. Routledge, 2011, pp. 46-73 [CFP 1327]

"My Intellectual Trajectory," March 2014