Abstract
General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tâtonnement processes for pure exchange economies, as well as further analogies implied by these.
Similar content being viewed by others
References
Arrow KJ, Debreu G. (1954) Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290
Arrow KJ, Hurwicz, L (1958) On the stability of the competitive equilibrium. I. Econometrica 26:522–552
Arrow KJ, Hurwicz, L (1960) Some remarks on the equilibria of economic systems. Econometrica 28: 640–646
Arrow KJ, Block, HD, Hurwicz, L (1959) On the stability of the competitive equilibrium. II. Econometrica 27: 82–109
Berger U, Hofbauer J (1998). The Nash dynamics. University of Vienna (mimeo)
Bomze IM, (1986). Noncooperative two-person games in biology: a classification. Int. J. Game Theory 15: 31–57
Brenner T (1999) Modelling Learning in Economics. Edward Elgar, Cheltenham, UK
Brown GW (1951) Iterative solutions of games by fictitious play. In: Koopmans TC (ed) Activity analysis of production and allocation, Wiley, New York, pp. 374–376
Brown GW, von Neumann, J (1950) Solutions of games by differential equations. Ann Math Stud 24: 73–79. Princeton University Press, Princeton, New Jersey
Crawford V (1974) Learning the optimal strategy in a zero-sum game. Econometrica 42: 885–891
Crawford V (1985) Learning behavior and mixed-strategy Nash equilibria. J. Econ Behav Organ 6:69–78
Darwin C (1859) On the origin of species by means of natural selection. J Murray, London, UK
Debreu G (1974) Excess demand functions. J. Math Econ 1: 15–23
Friedman D (1991) Evolutionary games in economics. Econometrica 59: 637–666
Fudenberg D, Levine DK (1998) The Theory of Learning in Games. MIT, Cambridge, Massachusetts
Gale D (1960) A note on revealed preference. Economica 27: 348–354
Gaunersdorfer A , Hofbauer J (1995) Fictitious play, Shapley polygons and the replicator equation. Games Econom Behav 11: 279–303
Hahn F (1982) Stability. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economy, vol II, North-Holland, Amsterdam, The Netherlands, pp. 745–793
Haigh J (1975) Game theory and evolution. Adv. Appl Probab 7: 8–11
Hammerstein P, R Selten, 1994, Game theory and evolutionary biology. In: Aumann RJ and Hart S (eds) Handbook of game theory 2, Elsevier, Amsterdam, The Netherlands
Harker PT, JS Pang (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math Program 48: 161–220
Hicks JR (1939) Value and capital. Oxford University Press, New York
Hildenbrand W (1994) Market demand. Princeton University Press, Princeton, New Jersey
Hodgson GM (1993) The Mecca of Alfred Marshall. Econ J 103: 406–415
Hofbauer J (1981) On the occurrence of limit cycles in the Volterra–Lotka equation. Nonlinear Anal 5: 1003–1007
Hofbauer J (1995) Stability for the best response dynamics. University of Vienna (mimeo)
Hofbauer J (2000) From Nash and Brown to Maynard Smith: equilibria, dynamics, and ESS. Selection 1: 81–88
Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge, UK
Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge, UK
Houthakker HS (1950) Revealed preference and the utility function. Economica 17: 159–174
Hurwicz L, Uzawa H (1971) On the integrability of demand functions. In: Chipman JS, Hurwicz L, Richter MK, Sonnenschein HF (eds.) Preferences, utility and demand. Harcourt Brace Jovanovich, New York
Israel G (1993) The emergence of biomathematics and the case of population dynamics—a revival of mechanical reductionism and Darwinism. Sci. Context 6: 469–509
John R (1996) Demand-supply systems, variational inequalities, and (generalized) monotone functions, Discussion paper A-530, SFB 303, Bonn University, Germany
John R (2000) A first order characterization of generalized monotonicity. Math Program 88: 147–155
Joosten R (1996) Deterministic evolutionary dynamics: a unifying approach. J Evol Econ 6: 313–324
Joosten R, Talman AJJ (1998) A globally convergent price adjustment process for exchange economies. J Math Econ 29: 15–26
Kihlstrom R, Mas-Colell A, Sonnenschein H (1976) The demand theory of the weak axiom of revealed preference. Econometrica 44: 971–978
Lewontin RC (1961) Evolution and the theory of games. J Theor Biol 1: 382–403
Lotka AJ (1924) Elements of mathematical biology (transl: 1956). Dover, New York
Mantel R (1974) On the characterization of aggregate excess demand. J Econ Theory 7: 348–353
Matsui A (1992) Best-response dynamics and socially stable strategies. J Econ Theory 57: 343–362 (1992)
Maynard SJ (1982) Evolution and the theory of games Cambridge University Press, Cambridge, UK
Maynard Smith J, Price GA (1973) The logic of animal conflict. Nature 246: 15–18
McKenzie LW (1960a) Stability of equilibrium and the value of positive excess demand. Econometrica 28: 606–617
McKenzie LW (1960b) Matrices with dominant diagonal and economic theory. In: Arrow KJ, Karlin S, Suppes P (eds) Mathematical methods in the social sciences (1959). Stanford University Press, Stanford, pp. 47–62
Mosak JL (1944) General equilibrium theory in international trade. Principia, Bloomington, Indiana
Nachbar JH (1990) Evolutionary selection dynamics in games: convergence and limit properties. Int J Game Theory 19: 59–89
Nash J (1950) Equilibrium points in n-person games. Proc Natl Acad Sci U S A 36: 48–49
Negishi T (1962) The stability of a competitive economy: a survey article. Econometrica 30: 635–669
Neumann J von, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, New Jersey
Nikaidô H (1959) Stability of equilibrium by the Brown-von Neumann differential equation. Econometrica 27: 654–671
Perko L (1991) Differential equations and dynamical systems Springer, Berlin Heidelberg New York
Peters H, P Wakker (1994) WARP does not imply SARP for more than two commodities. J Econ Theory 62: 152–160
Robinson J (1951) An iterative method of solving a game. Ann Math 54: 296–301
Rosenmüller J (1971) Über die Periodizitä tseigenschaften spieltheoretischer Lernprozesse. Z. Warscheinlichkeitstheor Verw Geb 17: 259–308
Rosser JB (1992) The dialogue between the economic and the ecologic theories of evolution. J Econ Behav Organ 17: 195–215
Samuelson P (1938) A note on the pure theory of consumer behavior. Economica 5: 61–71
Samuelson P (1941) The stability of equilibrium: comparative statics and dynamics. Econometrica 9: 97–120
Samuelson P (1947) Foundations of economic analysis. Harvard University Press, Cambridge, UK
Scarf H (1960) Some examples of the global instability of competitive equilibrium. Int Econ Rev 1: 157–172
Sonnenschein H (1972) Market excess demand functions. Econometrica 40: 549–563
Sonnenschein H (1973) Do Walras’ identity and continuity characterize community excess demand functions? J Econ Theory 6: 345–354
Taylor PD, LB Jonker (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40: 145–156
Uzawa H (1961) The stability of dynamic processes. Econometrica 29: 617–631
Van Damme ECC (1991) Stability and Perfection of Nash Equilibria. Springer, Berlin Heidelberg New York
Volterra V (1931) Leçons sur la Théorie Mathématique de la Lutte pour la Vie Gauthier-Villars, Paris, France
Wald A (1936) Über einige Gleichungssysteme der mathematischen Ökono-mie. Z. Nationalökon 7: 637–670
Walras L (1874) Élements d’Économie Politique Pure. Corbaz, Lausanne
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Joosten, R. Walras and Darwin: an odd couple?. J Evol Econ 16, 561–573 (2006). https://doi.org/10.1007/s00191-006-0037-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00191-006-0037-1