Selected Publications of David Gale

(1950) 'Compact Sets of Functions and Function Rings', Proceedings of the American Mathematical Society, 1, pp. 303-8. (1950) 'On Symmetric Games' (with H. W. Kuhn and A. W. Tucker), in H. W. Kuhn and A. W. Tucker (eds), Contributions to the Theory of Games, vol. I Annals of Mathematics Studies, 24 (Princeton: Princeton University Press) pp.81-7. (1950) 'Reductions of Game Matrices' (with H. W. Kuhn and A. W. Tucker), in H. W. Kuhn and A. W. Tucker (eds) , Contributions to the Theory of Games, vol. I, Annals of Mathematics Studies, 24 (Princeton: Princeton University Press) pp. 89-96. (1950) 'Solutions of Finite Two-Person Games' (with S. Sherman), in H. W. Kuhn and A. W. Tucker (eds), Contributions to the Theory of Games, vol. I Annals of Mathematics Studies, 24 (Princeton: Princeton University Press) pp. 37-40. (1951) 'Convex Polyhedral Cones and Linear Inequalities', in T. C. Koopmann (ed.), Activity Analysis of Production and Allocation, Cowles Commission Monograph, 13 (New York: John Wiley) pp. 287-97. (1951) 'Linear Programming and the Theory of Games' (with H. W. Kuhn and A. W. Tucker) in T. C. Koopmanns (ed.), Activity Analysis of Production and Allocation, Cowles Commission Monograph, 13 (New York: John Wiley) pp. 317-29. (1952) 'An Indeterminate Problem in Classical Mechanics', American Mathemat• ical Monthly, 59, pp. 291-5. (1953) 'On Inscribing n-Dimensional Sets in a Regular n-Simplex', Proceedings of the American Mathematical Society, 4, pp. 222-5. (1953) 'A Theory of N-Person Games with Perfect Information', Proceedings of the National Academy of Science, 39, pp. 496-50l. (1953) 'Infinite Games with Perfect Information' (with F. M. Stewart), in H. W. Kuhn and A. W. Tucker (eds), Contributions to the Theory of Games, vol. II, Annals of Mathematics Studies, 28 (Princeton: Princeton University Press) pp. 245--66. (1954) 'Linear Programming: An Introduction to the Problems and Methods' (with S. Dano), Nordisk Tidskrift for Teknisk Okonomi, pp. 5-3l. (1955) 'The Law of Supply and Demand', Mathematica Scandinavica, 3, pp. 155-69. (1956) 'The Closed Linear Model of Production', in H. W. Kuhn and A. W. Tucker (eds), Linear Inequalities and Related Systems, Annals of Mathematics Studies, 38 (Princeton: Princeton University Press) pp. 285-303. (1956) 'Mathematics and Economic Models', American Scientist, 44, pp. 33-44. (1956) 'The Basic Theorems of Real Linear Equations, Inequalities, Linear Programming, and Game Theory', Naval Research Logistics Quarterly, 3, pp. 19~200. (1956) 'Neighboring Vertices on a Convex Polyhedron', in H. W. Kuhn and A. W. Tucker (eds), Linear Inequalities and Related Systems, Annals of Mathemat• ics Studies, 38 (Princeton: Princeton University Press) pp. 255-63. (1957) 'Information in Games with Finite Resources', in M. Dresher, A. W.

358 Selected Publications of David Gale 359

Tucker and P. Wolfe (eds), Contributions to the Theory of Games, vol. 3, Annals of Mathematics Studies, 39 (Princeton: Princeton University Press) pp. 141-5. (1957) 'A Theorem on Flows in Networks', Pacific Journal of Mathematics, 7, pp. 1073-82. (1957) 'General Equilibrium for Linear Models', Rand Paper P-1156. (1957) 'Subalgebras of an Algebra with a Single Generator are Finitely Gener• ated', Proceedings of the American Mathematical Society, 8, pp. 929-30. (1957) 'The Theory of Matrix Games and Linear Economic Models' , Department of Mathematics, Brown University (course notes, mimeo). (1958) 'A Note on Polynomial and Separable Games' (with O. Gross), Pacific Journal of Mathematics, 8, pp. 735-41. (1959) 'Consensus of Subjective Probabilities: The Pari-Mutuel Method' (with E. Eisenberg), Annals of Mathematical Statistics, 30, pp. 165-8. (1959) 'Continous Convex Sets' (with V. L. Klee), Mathematica Scandinavica, 7, pp.379-91. (1959) 'On Transient Flows in Networks', Michigan Mathematical Journal, 6, pp. 59-63. (1960) 'A Note on Revealed Preference', Economica, 27 (108) pp. 348-54. (1960)The Theory of Linear Economic Models (New York: McGraw-Hill). (1962) 'College Admissions and the Stability of Marriage' (with L. S. Shapley), American Mathematical Monthly, 69, pp. 9-15. (1963) 'A Note on Global Instability of Competitive Equilibrium', Naval Re• search Logistics Quarterly, 10, pp. 81-7. (1963) 'On Lipschitzian Mappings of Convex Bodies', Convexity, Proceedings of Symposia in Pure Mathematics, 7, American Mathematical Society, pp.221-4. (1963) 'Neighborly and Cyclic Polytopes', Convexity, Proceedings of Symposia in Pure Mathematics, 7, American Mathematical Society, pp. 225-32. (1964) 'On Equilibrium for a Multi-Sector Model of Income Propagation', Inter• national Economic Review, 5, pp. 185-200. (1964) 'On the Number of Faces of a Convex Polytope', Canadian Journal of Mathematics, 16, pp. 12-17. (1964) 'The Jacobian Matrix and Global Univalence of Mappings' (with H. Nikaido), Mathematische Annalen, 2, pp. 81-93. (1965) 'Optimal Programs for Sequential Investment', (Providence: Brown Uni• versity Press). (1967) 'A Geometric Duality Theorem with Economic Applications', The Review of Economic Studies, 34, pp. 19-24. (1967) 'On Optimal Development in a Multi-Sector Economy', The Review of Economic Studies, 34, Symposium on Infinite Programmes, pp. 1-18. (1968) 'A Mathematical Theory of Optimal Economic Development', Bulletin of the American Mathematical Society, 74, pp. 207-23. (1968) 'Optimal Assignments in an Ordered Set: An Application of Matroid Theory', Journal of Combinatorial Theory, 4, pp. 176--80. (1968) 'Analysis of a One-Good Model of Economic Development' (with W. R. Sutherland), in G. B. Dantzig and A. F. Veinott Jr, (eds), Mathematics of the Decision Sciences, Part 2, Lectures in Applied Mathematics, 12, American Mathematical Society, pp. 12~36. (1968) 'Convex Functions on Convex Polytopes' (with V. Klee and R. T. Rocka• fellar), Proceedings of the American Mathematical Society, 19, pp. 867-73. (1969) 'How to Solve Linear Inequalities', American Mathematical Monthly, 76, pp.589-99. 360 Selected Publications of David Gale

(1969) 'Optimal Growth Under Factor Augmenting Progress' (with W. Brock), Journal of Economic Theory, 1, pp. 229-43. (1970) 'The Jeep Once More or Jeeper by the Dozen', American Mathematical Monthly, 77, pp. 493-50l. (1970) 'Nonlinear Duality and Qualitative Properties of Optimal Growth', in J. Abadie (ed.), Integer and Nonlinear Programming (Amsterdam: North• Holland) pp. 309-19. (1971) 'General Equilibrium with Imbalance of Trade', Journal of International Economics, 1, pp. 141-58. (1971) 'Optimal Strategy for Serving· in Tennis', Mathematics Magazine, 44, pp. 197-9. (1972) 'A Phenomenon in the Theory of Sorting' (with R. M. Karp), Journal of Computer and System Sciences, 6, pp. 103-15. (1972) 'On Equilibrium Growth of Dynamic Economic Models', Mathematical Topics in Economic Theory and Computation, Society for Industrial and Applied Mathematics, (Philadelphia) pp. 89-98. (1972) Comment, Econometrica, 40, pp. 391-2. (1973) 'Pure Exchange Equilibrium of Dynamic Economic Models', Journal of Economic Theory, 6, pp. 12-36. (1973) 'On the Theory of Interest', American Mathematical Monthly, 80, pp. 853-68. (1974) 'Exchange Equilibrium and Coalitions: An Example', Journal of Math• ematical Economics, 1, pp. 63-6. (1974) 'The Trade Imbalance Story', Journal of International Economics, 4, pp. 119-37. (1974) 'A Curious Nim-Type Game', American Mathematical Monthly, 81, pp. 876-9. (1975) 'An Equilibrium Existence Theorem for a General Model without Or• dered Preferences' (with A. Mas-Colell), Journal of Mathematical Economics, 2, pp.9-15. (1975) 'Note and Comment on the Interest Rate Theorems of Malinvaud and Starrett' (with R. Rockwell), Econometrica, 43, pp. 347-60. (1975) 'An Extension of Cass' Characterization of Infinite Efficient Production Programs' (with L. Benveniste), Journal of Economic Theory, 10, pp. 229-38. (1975) 'Unique Reducibility of Subsets of Commutative Topological Groups and Semi-Groups' (with V. L. Klee), Mathematica Scandinavica, 36, pp. 174-98. (1976) 'The Linear Exchange Model', Journal of Mathematical Economics, 3, pp. 205-9. (1976) 'The Malinvaud Eigenvalue Lemma: Correction and Amplification' (with R. Rockwell), Econometrica, 44, pp. 1323-4. (1977) 'Piecewise Linear Exchange Equilibrium', Journal of Mathematical Econ• omics, 4, pp. 81-6. (1977) 'Dynamic Behavior of a Simple Neoclassical Model with Wealth and Capital Unequal', Journal of Economic Theory, 15, pp. 398-409. (1978) 'On the Role of Complete, Transitive Preferences in Equilibrium Theory' (with A. Mas-Colell), in G. SchwOdiauer (ed.), Equilibrium and Disequilibrium in Economic Theory (Boston: D. Reidel Publishing Co.) pp. 7-14. (1979) 'Tone Perception and Decomposition of Periodic Functions', American Mathematical Monthly, 86, pp. 36-42. (1979) 'An Algorithm for a Piecewise Linear Model of Trade and Production with Negative Prices and Bankruptcy' (with G. B. Dantzig and B. C. Eaves), Mathematical Programming, 16, pp. 190-209. Selected Publications of David Gale 361

(1979) 'Optimization Methods for Solving Nonoptimization Problems', in C. V. Coffman and G. J. Fix (eds), Constructive Approaches to Mathematical Models (New York: Academic Press) pp. 327-34. (1979) 'The Game of Hex and the Brouwer Fixed-Point Theorem', American Mathematical Monthly, 86, pp. 818-27. (1979) 'Corrections to an Equilibrium Theorem for a General Mode witpout Ordered Preferences' (with A. Mas-Colell), Journal of Mathematical Economics, 6, pp. 297-8. (1979) 'Fair Division of a Random Harvest. The Finite Case' (with J. Sobel), General Equilibrium Growth and Trade, Essays in Honor of Lionel McKenzie (New York: Academic Press) pp. 193-8. (1981) 'Substitutes and Complements in Network Flow Problems' (with T. Poli• tof), Discrete Applied Mathematics, 3, pp. 175-86. (1982) 'On Optimal Distribution of Output from a Jointly Owned Resource' (with J. Sobel), Journal of Mathematical Economics, 9, pp. 51-9. (1982) 'Nim-Type Games' (with A. Neyman), International Journal of Game Theory, 11 (1) pp. 17-20. (1982) 'On Optimal Operation of a Jointly Owned Enterprise' (with H. Ma• chado), Journal of Mathematical Economics, 10, pp. 269-78. (1982) 'Efficiency', in M. Hazewinkel and A. H. G. Rinnooy Kan (eds), Current Developments in the Interface: Economics, Econometrics, Mathematics (Boston: D. Reidel Publishing Co.) pp. 75-86. (1982) 'Two Remarks on the Mendelsohn-Dulmage Theorem' (with A. J. Hoff• man), in E. Mendelsohn (ed.), Algebraic and Geometric Combinatorics, Annals of Discrete Mathematics, vol. 15 (Amsterdam: North-Holland) pp. 171-7. (1984) 'Equilibrium in a Discrete Exchange Economy with Money', International Journal of Game Theory, 13(1) pp. 61-4. (1985) 'Ms. Machiavelli and the Stable Matching Problem' (with M. Sotomayor), American Mathematical Monthly, 92 (4), pp. 261-8. (1985) 'Some Remarks on the Stable Matching Problem' (with M. Sotomayor), Discrete Applied Mathematics, 11, pp. 223-32. (1985) 'The Strategy Structure of Two-Sided Matching Markets' (with G. De• mange), Econometrica, 53(4) pp. 873-88. (1986) 'Multi-Item Auctions' (with G. Demange and M. Sotomayor), Journal of Political Economy, 94(4) pp. 863-72. (1987) 'A Further Note on the Stable Matching Problem' (with G. Demange and M. Sotomayor), Discrete Applied Mathematics, 16, pp. 217-22. (1987) 'The Classification of I-manifolds: A Take-Home Exam', American Mathematical Monthly, 94, pp. 171-5. (1989) 'The Truth and Nothing but the Truth', Mathematical Intellegencer (July) pp.62-7.