History of Fixed Point Theorems in General Equilibrium Theory — Internet Resources

Original Papers and Historical Accounts on JSTOR

Report of the Chicago Meeting, December 27—29, 1952, Econometrica, Vol 21, No. 3 (Jul., 1953), pp. 463-490.

McKenzie, Arrow and Debreu gave talks on their proofs of the existence of equilibria in general equilibrium theory at a meeting of the Econometric Society held in Chicago, December 27—29, 1952. Following McKenzie's talk, Debreu observed that the results were analogous to those that he had presented in an earlier talk.

Lionel McKenzie, On Equilibrium in Graham's Model of World Trade and Other Competitive Systems, Econometrica, Vol 22, No. 2 (Apr., 1954), pp. 147-161.

This is the original paper by Lionel McKenzie, published in Econometrica in 1954, containing the existence theorem for economic equilibria.

Kenneth J. Arrow and Gerard Debreu, Existence of an Equilibrium for a Competitive Economy, Econometrica, Vol. 22, No. 3. (Jul., 1954), pp.265-290.

This is the original paper by Kenneth Arrow and Gérard Debreu, published in Econometrica in 1954, containing the existence theorem for economic equilibria.

Lionel McKenzie, The Classical Theorem on Existence of Competitive Equilibrium (Econometrica, Vol 49, No. 4 (Jul 1981), pp. 819-841.)

This is a later paper by Lionel McKenzie, published in Econometrica in 1981, refining and extending the existence theorem for economic equilibria.

Hal R. Varian Gerard Debreu's Contribution to Economics (The Scandinavian Journal of Economics Vol 86, No. 1 (Mar. 1984) 4—14.)

Hal Varian is Chief Economist at Google, and is an Emeritus Professor at the University of California at Berkeley. He has authored textbooks in Intermediate Microeconomics and Microeconomic Analysis

Alan F. Beardon Debreu's Gap Theorem (Economic Theory, Vol No. 1, (Jan. 1992) pp. 150—152.

This paper was written by a professor of mathematics at the University of Cambridge, now retired, with reseach interests in analysis, and, in particular, complex analysis and the theory of Riemann surfaces.

Darrell Duffie and Hugo Sonnenschein, Arrow and General Equilibrium Theory, Journal of Economic Literature, Vol 27, No. 2 (Jun. 1989), pp. 565-598.

This is a review of Kenneth J. Arrow, Collected Papers of Kenneth J. Arrow, Vol 2, General Equilibrium, Harvard U. Press, Cambridge, MA, 1983.

Bruce Caldwell (2003) Review of "How Economics became a Mathematical Science" by E. Roy Weintraub (Southern Economic Journal, 69(4) (2003), 1011—1015.

>Kenneth Arrow (2011), Gérard Debreu: 4 July 1921 to 31 December 2004 (Proceedings of the American Philosophical Society, 155(3) (Sep. 2011) 319—325)

Original Papers and Historical Accounts relevant to Existence Proofs of General Equilibrium available outside JSTOR

John Nash, Equilibrium points in n person games, Proceedings of the National Academic of Sciences of the United States of America, 36(1) (1950), 48—49.

This is the very short paper in which John Nash published his existence theorem for equilibria in noncooperative n person games. (This resource may not be generally available outside institutions that subscribe to PNAS online.)

David Gale, The Law of Supply and Demand, Mathematica Scandinavica, 3 (1955), 155—169.

David Gale published a proof of the existence of equilibria in general equilibrium theory obtained independently of the analogous results obtained by McKenzie, Arrow, Debreu and Nikaido.

Stephen Smale (1976), Dynamics in General Equilibrium Theory (The American Economic Review, 66(2), 288—294).

E. Roy Weintraub and Ted Gayer (2001), Equilibrium Proofmaking (Journal of the History of Economic Thought, 23(4) (2001), 421—442.

This paper discusses in detail events surrounding the refereeing and publication of the paper by Arrow and Debreu in 1954.

Aiko Ikeo (2009), How Modern Algebra was used in Economic Science in the 1950s: Breaking the Glass Wall to the Scientific Acceptance (General Equilibrium Theory (2): the Existence Question) (Prepared for the History of Political Economic Seminar, Duke University, and also presented at the History of Economics Society Annual Meeting, in Denver, Colorado, in 2009)

This essay, by Aiko Ikeo (Duke University / Waseda University), author of A history of economic science in Japan: the internationalization of economics in the twentieth century (ISBN: 9780415634274), focusses in particular on the proof of the existence of equilibria by Hukukane Nikaido, using the Kakutani Fixed Point Theorem, and discusses the background to the publication of Nikaido's proof in Metroeconomica in 1956.

E. Roy Weintraub (2011), Retrospectives: Lionel W. McKenzie and the Proof of the Existence of a Competitive Equilibrium. (Journal of Economic Perspectives, 25(2), 199—215)

This paper traces the history of Lionel W. McKenzie's proof of the existence of equilibria, using the Kakutani Fixed Point Theorem, and discusses the background to the publication of McKenzie's proof in Econometrica in 1954.

Till Düppe (2010), Debreu's apologies for mathematical economics after 1983, (Erasmus Journal for Philosophy and Economics, 3(1), 1—32)

This essay discusses the significance of Debreu's axiomatic approach to economic theory.

S. Abu Turab Rizvi (2015), Review of Till Düppe and E. Roy Weintraub's Finding Equilibrium: Arrow, Debreu, McKenzie and the problem of scientific credit. (Erasmus Journal for Philosophy and Economics, 8(1), pp. 110—115.

A book review.

Original Papers and Historical Accounts relevant to the History of Game Theory

John Nash, Equilibrium points in n person games, Proceedings of the National Academic of Sciences of the United States of America, 36(1) (1950), 48—49.

This is the very short paper in which John Nash published his existence theorem for equilibria in noncooperative n person games. (This resource may not be generally available outside institutions that subscribe to PNAS online.)

Pierre Courtois, Rabia Nessah, Tarik Tazdaït, How to play the games? Nash versus Berge behavious rules (LAMETA, Laboratoire Montpelliérain d'Economie Théorique et Appliquée, Document de Recherche, DR n^o 2011-05, 2011).

This document discusses the history of the concept of Berge Equilibrium, based on work of Claude Berge. This is an equilibrium strategy where a given player achieves maximum utility when all other players adopt the equilibrium strategy. This equilibrium concept is distinct from that of a Nash equilibrium which, if adopted by all players of the game, would motivate no player to change strategy to achieve a higher utility.

Mathematical Economics and The Differential Approach to General Equilibrium Theory.

Alan G. White (1993), It's a Maths Maths World!

This essay by Dr. Alan G. White ( Managing Principal, The Analysis Group) was published (when an undergraduate student) in the Student Economic Review (Department of Economics, TCD) in 1993. It summarizes the history of interactions between the disciplines of mathematics and economics, and discusses the conclusions of surveys of attitudes within the economics profession regarding the use of mathematics in the study of economics.

Alan G. White (1994), A Differential Approach to General Equilibrium

This essay by Dr. Alan G. White ( Managing Principal, The Analysis Group) was published (when a postgraduate student) in the Student Economic Review (Department of Economics, TCD) in 1994. It surveys the history of the application of techniques from the theories of differentiable manifolds and differential topology to the study of general equilibrium theory.