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Perfect Competition

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Abstract

This article attempts a critical appraisal of the literature on perfect competition as it has evolved since the work of Debreu–Scarf and Aumann in the 1960s, following papers of Debreu–Scarf and Aumann. It focuses on mathematical techniques that have been garnered to cope with the presuppositions of the classical theory relating to finitude, convexity and agent-independence.

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Bibliography

  • Aliprantis, C.D., B. Cornet, and R. Tourky. 2002. Economic equilibrium: Optimality and price decentralization. Positivity 6: 205–241.

    Article  Google Scholar 

  • Aliprantis, C.D., M. Florenzano, and R. Tourky. 2006. Production equilibria. Journal of Mathematical Economics 42: 406–421.

    Article  Google Scholar 

  • Anderson, R.M. 1978. An elementary core equivalence theorem. Econometrica 46: 1483–1487.

    Article  Google Scholar 

  • Anderson, R.M. 1991. Non-standard analysis with applications to economics. In Handbook of mathematical economics, ed. W. Hildenbrand and H. Sonnenschein, vol. 4. New York: North-Holland.

    Google Scholar 

  • Anderson, R.M. 1992. The core in perfectly competitive economies. In Handbook of game theory with economic applications, ed. R.J. Aumann and S. Hart, vol. 1. Amsterdam: North-Holland.

    Google Scholar 

  • Anderson, R.M. 1998. Convergence of the Aumann–Davis–Maschler and Geanakopolos bargaining sets. Economic Theory 11: 1–37.

    Article  Google Scholar 

  • Anderson, R.M., M.A. Khan, and S. Rashid. 1982. Approximate equilibria with bounds independent of preferences. Review of Economic Studies 49: 473–475.

    Article  Google Scholar 

  • Anderson, R.M., and R. Raimondo. 2006. Equilibrium in continuous-time financial markets: Endogenously dynamically complete markets, Working paper. Berkeley: University of Berkeley.

    Google Scholar 

  • Araujo, A., V.F. Martins-da-Rocha, and P. Monteiro. 2004. Equilibria in reflexive Banach lattices with a continuum of agents. Economic Theory 24: 469–492.

    Article  Google Scholar 

  • Armstrong, T.E., and K. Prikry. 1981. Liapunoff’s theorem for nonatomic, finitely additive, bounded, finite-dimensional vector-valued measures. Transactions of the American Mathematical Society 266: 499–514. Erratum in the same journal (1982), 272, 809.

    Google Scholar 

  • Armstrong, T., and M.K. Richter. 1986. Existence of nonatomic core-Walras allocation. Journal of Economic Theory 38: 137–159.

    Article  Google Scholar 

  • Arrow, K.J. 1986. Economic theory and the hypothesis of rationality. Journal of Business 59: S385–S399.

    Article  Google Scholar 

  • Aumann, R.J. 1964. Markets with a continuum of traders. Econometrica 32: 39–50.

    Article  Google Scholar 

  • Aumann, R.J. 1966. Existence of competitive equilibria in markets with a continuum of traders. Econometrica 34: 1–17.

    Article  Google Scholar 

  • Avallone, A., and A. Basile. 1998. Lyapunov–Richter theorem in B-convex spaces. Journal of Mathematical Economics 30: 109–118.

    Article  Google Scholar 

  • Balder, E.J. 2000. Incompatibility of usual conditions for equilibrium existence in continuum economies without ordered preferences. Journal of Economic Theory 93: 110–117.

    Article  Google Scholar 

  • Balder, E.J. 2007a. Comments on purification in continuum games. International Journal of Game Theory 37.

    Google Scholar 

  • Balder, E.J. 2007b. More on equilibria in competitive markets with externalities and a continuum of agents. Journal of Mathematical Economics 44.

    Google Scholar 

  • Basile, A., and M.G. Graziano. 2001. Restricted coalition formation mechanisms in finitely-additive economies. Journal of Mathematical Economics 36: 219–240.

    Article  Google Scholar 

  • Bonnisseau, J.M. 2002. The marginal pricing rule in economies with infinitely many commodities. Positivity 6: 275–296.

    Article  Google Scholar 

  • Bonnisseau, J.M., and Cornet, B. 2006. Existence of equilibria with a tight marginal pricing rule. Cahier de la MSE, Université Paris 1.

    Google Scholar 

  • Brown, D.J. 1976. Existence of competitive equilibrium in a non standard exchange economy. Econometrica 44: 537–547.

    Article  Google Scholar 

  • Brown, D.J., and M.A. Khan. 1980. An extension of the Brown–Robinson equivalence theorem. Applied Mathematics and Computation 6: 167–175.

    Article  Google Scholar 

  • Brown, D.J., and A. Robinson. 1975. Non standard exchange economies. Econometrica 43: 41–55.

    Article  Google Scholar 

  • Buchanan, J.M. 1987. Economics: Between predictive science and moral philosophy. College Station: Texas A&M University Press.

    Google Scholar 

  • Cassels, J.W.S. 1975. Measures of the non-convexity of sets and the Shapley–Folkman–Starr theorem. Mathematical Proceedings of the Cambridge Philosophical Society 78: 433–436.

    Article  Google Scholar 

  • Cornet, B., and M. Topuzu. 2005. Existence of equilibria for economies with externalities and a measure space of consumers. Economic Theory 26: 397–421.

    Article  Google Scholar 

  • Debreu, G. 1959. The theory of value. New York: Wiley.

    Google Scholar 

  • Debreu, G. 1967. Preference functions on measure spaces of economic agents. Econometrica 35: 111–122.

    Article  Google Scholar 

  • Debreu, G., and H. Scarf. 1963. A limit theorem on the core of an economy. International Economic Review 4: 235–246.

    Article  Google Scholar 

  • Diestel, J., and J.J. Uhl. 1977. Vector measures. Providence: American Mathematical Society.

    Book  Google Scholar 

  • Duffie, D., and Y.N. Sun. 2007. Existence of independent random matching. Annals of Applied Probability 17: 386–419.

    Article  Google Scholar 

  • Edgeworth, F.Y. 1881. Mathematical psychics. London: Kegan-Paul.

    Google Scholar 

  • Farrell, M.J. 1959. The convexity assumption in the theory of competitive markets. Journal of Political Economy 67: 377–391.

    Article  Google Scholar 

  • Fenchel, H. 1951. Convex cones, sets and functions, Lecture notes. Princeton: Princeton University Press.

    Google Scholar 

  • Foley, D. 1970. Lindahl’s solution and the core of an economy with public goods. Econometrica 38: 66–72.

    Article  Google Scholar 

  • Forges, F., A. Heifetz, and E. Minelli. 2001. Incentive compatible core and competitive equilibria in differential information economies. Economic Theory 18: 349–365.

    Article  Google Scholar 

  • Forges, F., E. Minelli, and R. Vohra. 2002. Incentives and the core of an exchange economy: A survey. Journal of Mathematical Economics 38: 1–41.

    Article  Google Scholar 

  • Gabszewicz, J., and B. Shitovitz. 1992. The core in imperfectly competitive economies. In Handbook of game theory with economic applications, ed. R.J. Aumann and S. Hart, vol. 1. Amsterdam: North-Holland.

    Google Scholar 

  • Geller, W. 1986. A improved bound for approximate equilibria. Review of Economic Studies 53: 307–308.

    Article  Google Scholar 

  • Hamano, T. 1989. On the non-existence of the marginal cost pricing equilibrium and the Ioffe normal cone. Zeitschrift für National Ökonomie 50: 47–53.

    Google Scholar 

  • Hammond, P.J. 1993. Irreducibility, resource-relatedness, and survival in equilibrium with individual non-convexities. In General equilibrium, growth and trade II, ed. R. Becker, M. Boldrin, R. Jones, and W. Thomson. New York: Academic Press.

    Google Scholar 

  • Hammond, P.J. 1995. Four characterizations of constrained Pareto efficiency in continuum economies with widespread externalities. Japanese Economic Review 46: 103–124.

    Article  Google Scholar 

  • Hammond, P.J., M. Kaneko, and M.H. Wooders. 1989. Continuum economies with finite coalitions: Core equilibria and widespread externalities. Journal of Economic Theory 49: 113–134.

    Article  Google Scholar 

  • Hart, S. 2002. Values of perfectly competitive economies. In Handbook of game theory with economic applications, ed. R.J. Aumann and S. Hart, vol. 3. Amsterdam: North-Holland.

    Google Scholar 

  • Hayek, F.A. 1948. Individualism and economic order. Chicago: Chicago University Press.

    Google Scholar 

  • Herves-Beloso, C., E. Moreno-Garcia, and N.C. Yannelis. 2005. An equivalence theorem for a differential information economy. Journal of Mathematical Economics 41: 844–856.

    Article  Google Scholar 

  • Hicks, J.R. 1939. The foundations of welfare economics. Economic Journal 49: 696–712. Also, Prefatory note to the 1984 reprint in Wealth and welfare: Collected essays in economic theory, vol. 1. Oxford: Basil Blackwell.

    Google Scholar 

  • Hildenbrand, W. 1974. Core and equilibria of a large economy. Princeton: Princeton University Press.

    Google Scholar 

  • Hotelling, H. 1938. The general welfare in relation to problems of taxation and of railway and utility rates. Econometrica 6: 242–269.

    Article  Google Scholar 

  • Hurwicz, L. 1972. On informationally decentralized systems. In Decision and organization, ed. C.B. McGuire and R. Radner. Amsterdam: North-Holland.

    Google Scholar 

  • Ingrao, B., and G. Israel. 1987. La Mano invisibile. Roma-Bari: Gius. Laterza & Figli Spa. English translation, The invisible hand: Economic equilibrium in the history of science. Cambridge: MIT Press, 1990.

    Google Scholar 

  • Jackson, M., and A. Manelli. 1997. Approximate competitive equilibria in large economies. Journal ofEconomic Theory 77: 354–376.

    Article  Google Scholar 

  • Jordan, J., and R. Radner. 1982. Rational expectations in microeconomic models: An overview. Journal of Economic Theory 26: 201–223.

    Article  Google Scholar 

  • Kaneko, M., and M.H. Wooders. 1986. The core of a game with a continuum of players and finite coalitions: The model and some results. Mathematical Social Sciences 12: 105–137.

    Article  Google Scholar 

  • Kaneko, M., and M.H. Wooders. 1989. The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies. Journal of Economic Theory 49: 135–168.

    Article  Google Scholar 

  • Kaneko, M., and M.H. Wooders. 1994. Widespread externalities and perfectly competitive markets: Examples. In Imperfections and behavior in economic organizations, ed. R.P. Gilles and P.H.M. Ruys. Boston: Kluwer.

    Google Scholar 

  • Kaneko, M., and M.H. Wooders. 1996. The nonemptiness of the f-core of a game without side-payments. International Journal of Game Theory 25: 245–258.

    Article  Google Scholar 

  • Khan, M.A. 1974. Some remarks on the core of a ‘large’ economy. Econometrica 42: 633–642.

    Article  Google Scholar 

  • Khan, M.A. 1975. Some approximate equilibria. Journal of Mathematical Economics 2: 63–86.

    Article  Google Scholar 

  • Khan, M.A. 1988. Ioffe’s normal cone and the foundations of welfare economics: An example. Economics Letters 28: 15–19.

    Article  Google Scholar 

  • Khan, M.A. 1993. Lionel McKenzie and the existence of competitive equilibrium. In General equilibrium, growth and trade II, ed. R. Becker, M. Boldrin, R. Jones, and W. Thomson. New York: Academic Press.

    Google Scholar 

  • Khan, M.A. 1998. Representation, language and theory: Georgescu-Roegen on methods of economic science. Paper presented at the Colloque International L’Oeuvre Scientifique de Nicholas Georgescu-Roegen, Strasbourg, 7–9 November.

    Google Scholar 

  • Khan, M.A. 1999. The Mordukhovich normal cone and the foundations of welfare economics. Journal of Public Economic Theory 1: 309–338.

    Article  Google Scholar 

  • Khan, M.A., and N. Papageorgiou. 1987. On Cournot–Nash equilibrium in generalized qualitative games with an atomless measure space of players. Proceedings of the American Mathematical Society 100: 505–510.

    Article  Google Scholar 

  • Khan, M.A., and N.T. Peck. 1989. On the interiors of production sets in infinite dimensional spaces. Journal of Mathematical Economics 18: 29–39.

    Article  Google Scholar 

  • Khan, M.A., and S. Rashid. 1976. Limit theorems on cores with costs of coalition formation, Johns Hopkins working paper No. 24. Abridged version published as ‘A limit theorem for an approximate core of a large but finite economy’, Economics Letters 1 (1978): 297–302.

    Google Scholar 

  • Khan, M.A., and S. Rashid. 1982. Approximate equilibria in markets with indivisible commodities. Journal of Economic Theory 28: 82–101.

    Article  Google Scholar 

  • Khan, M.A., and Y.N. Sun. 1996. Non-atomic games on Loeb spaces. Proceedings of the National Academy of Sciences of the United States of America 93: 15518–15521.

    Article  Google Scholar 

  • Khan, M.A., and Y.N. Sun. 1997a. The capital-asset-pricing model and arbitrage pricing theory: A unification. Proceedings of the National Academy of Sciences of the United States of America 94: 4229–4232.

    Article  Google Scholar 

  • Khan, M.A., and Y.N. Sun. 1997b. On Loeb measure spaces and their significance for non-cooperative game theory. In Current and future directions in applied mathematics, ed. M. Alber, B. Hu, and J. Rosenthal. Berlin: Birkhäuser.

    Google Scholar 

  • Khan, M.A., and Y.N. Sun. 1999a. Weak measurability and characterizations of risk. Economic Theory 13: 441–460.

    Google Scholar 

  • Khan, M.A., and Y.N. Sun. 1999b. Non-cooperative games on hyperfinite Loeb spaces. Journal of Mathematical Economics 31: 455–492.

    Article  Google Scholar 

  • Khan, M.A., and Y.N. Sun. 2002. Non-cooperative games with many players. In Handbook of game theory with economic applications, ed. R.J. Aumann and S. Hart, vol. 3. Amsterdam: North-Holland.

    Google Scholar 

  • Khan, M.A., and R. Vohra. 1984. Equilibrium in abstract economies with out ordered preferences and with a measure space of agents. Journal of Mathematical Economics 13: 133–142.

    Article  Google Scholar 

  • Khan, M.A., and R. Vohra. 1985. On the existence of Lindahl equilibria in economies with a measure space of non-transitive consumers. Journal of Economic Theory 36: 319–332.

    Article  Google Scholar 

  • Khan, M.A., and R. Vohra. 1987. Lindahl–Hotelling equilibria. Journal of Public Economics 34: 143–158.

    Article  Google Scholar 

  • Khan, M.A., and N.C. Yannelis. 1991. Equilibrium theory in infinite dimensional spaces. New York: Springer.

    Book  Google Scholar 

  • Khan, M.A., K.P. Rath, and Y.N. Sun. 2006. The Dvoretzky–Wald–Wolfowitz theorem and purification in atomless finite-action games. International Journal of Game Theory 34: 91–104.

    Article  Google Scholar 

  • Kluvanek, I., and G. Knowles. 1976. Vector measures and control systems. Amsterdam: North-Holland.

    Google Scholar 

  • Koopmans, T.C. 1961. Convexity assumptions, allocative efficiency, and competitive equilibrium. Journal of Political Economy 69: 478–479.

    Article  Google Scholar 

  • Koopmans, T.C. 1974. Is the theory of competitive equilibrium with it? American Economic Review 69: 325–329.

    Google Scholar 

  • Loeb, P.A. 1973. A combinatorial analog of Lyapunov’s theorem for infinitesimally generated atomic vector measures. Proceedings of the American Mathematical Society 39: 585–586.

    Google Scholar 

  • Loeb, P.A. 1975. Conversion from nonstandard to standard measure spaces and applications in probability theory. Transactions of the American Mathematical Society 211: 113–122.

    Article  Google Scholar 

  • Loeb, P.A., and Y.N. Sun. 2006. Purification of measure-valued maps. Illinois Journal of Mathematics 50: 747–762.

    Google Scholar 

  • Loeb, P.A., and M. Wolff. 2000. Nonstandard analysis for the working mathematician. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Majumdar, M., and V. Rotar. 2000. Equilibrium prices in a random exchange economy with dependent agents. Economic Theory 15: 531–550.

    Article  Google Scholar 

  • Makowski, L., and J.M. Ostroy. 2001. Perfect competition and the creativity of the market. Journal of Economic Literature 39: 479–535.

    Article  Google Scholar 

  • Martins-da-Rocha, V.F. 2003. Equilibria in large economies with a separable Banach commodity space and non-ordered preferences. Journal of Mathematical Economics 39: 863–889.

    Article  Google Scholar 

  • Martins-da-Rocha, V.F. 2004. Equilibria in large economies with differentiated commodities and non-ordered preferences. Economic Theory 23: 529–552.

    Article  Google Scholar 

  • Mas-Colell, A. 1986. The price equilibrium existence problem in topological vector lattices. Econometrica 54: 1039–1054.

    Article  Google Scholar 

  • Mas-Colell, A., and W.R. Zame. 1991. Equilibrium theory in infinite dimensional spaces. In Handbook of mathematical economics, ed. W. Hildenbrand and H. Sonnenschein, vol. 4. Amsterdam: North-Holland.

    Google Scholar 

  • McKenzie, L.W. 2002. Classical general equilibrium theory. Cambridge: MIT Press.

    Google Scholar 

  • Mirowski, P. 2002. Machine dreams. Cambridge: Cambridge University Press.

    Google Scholar 

  • Mordukhovich, B.S. 2006. Variational analysis and generalized differentiation, I & II. Berlin: Springer.

    Google Scholar 

  • Morgan, M. 1993. Competing notions of ‘competition’ in late nineteenth-century American economics. History of Political Economy 25: 563–604.

    Article  Google Scholar 

  • Noguchi, M. 2005. Interdependent preferences with a continuum of agents. Journal of Mathematical Economics 41: 665–686.

    Article  Google Scholar 

  • Noguchi, M., and W.R. Zame. 2006. Competitive markets with externalities. Theoretical Economics 1: 143–166.

    Google Scholar 

  • Novshek, W., and H. Sonnenschein. 1983. Walrasian equilibria as limits of noncooperative equilibria. Journal of Economic Theory 30: 171–187.

    Article  Google Scholar 

  • Otani, Y., and J. Sicilian. 1977. Externalities and problems of nonconvexity and overhead costs in welfare economics. Journal of Economic Theory 14: 239–252.

    Article  Google Scholar 

  • Pigou, A.C. 1932. The economics of welfare, 4th ed. London: Macmillan. 1st edn, 1920.

    Google Scholar 

  • Podczeck, K. 1997. Markets with infinite commodities and a continuum of agents with non-convex preferences. Economic Theory 9: 385–426.

    Article  Google Scholar 

  • Podczeck, K. 2001. Core and Walrasian equilibria when agents’ characteristics are extremely dispersed. Economic Theory 22: 699–725.

    Article  Google Scholar 

  • Podczeck, K. 2004. On Core-Walras equivalence in Banach spaces when feasibility is defined by the Pettis integral. Journal of Mathematical Economics 40: 429–463.

    Article  Google Scholar 

  • Radner, R. 1967. Equilibre des marchés á terme et au comptant en cas d’incertitude. Cahiers d’econométrie 9: 30–47.

    Google Scholar 

  • Radner, R. 1982. Equilibrium under uncertainty. In Handbook of mathematical economics, ed. K.J. Arrow and M.D. Intriligator, vol. 2. New York: North-Holland.

    Google Scholar 

  • Radner, R. 1991. Intertemporal general equilibrium. In Value and capital: Fifty years later, ed. L.W. McKenzie and S. Zemagni. London: Macmillan.

    Google Scholar 

  • Rashid, S. 1987. Economies with many agents. Baltimore: Johns Hopkins Press.

    Google Scholar 

  • Rockafellar, R.T. 1970. Convex Analysis. Princeton: Princeton University Press.

    Book  Google Scholar 

  • Rockafellar, R.T., and J.-B. Wets. 1998. Variational analysis. New York: Springer.

    Book  Google Scholar 

  • Rudin, W. 1974. Real and complex analysis. New York: McGraw-Hill Book Co..

    Google Scholar 

  • Samuelson, P.A. 1954. The pure theory of public expenditures. Review of Economics and Statistics 36: 387–389.

    Article  Google Scholar 

  • Serrano, R., and O. Volij. 2000. Walrasian allocations without price-taking behavior. Journal of Economic Theory 95: 79–106.

    Article  Google Scholar 

  • Serrano, R., R. Vohra, and O. Volij. 2001. On the failure of core convergence with asymmetric information. Econometrica 69: 1685–1696.

    Article  Google Scholar 

  • Shannon, C. 1999. Increasing returns in infinite horizon economies. Review of Economics Studies 64: 73–96.

    Article  Google Scholar 

  • Shapley, L.S. 1975. An example of a slow-converging core. International Economic Review 16: 345–351.

    Article  Google Scholar 

  • Starr, R.M. 1969. Quasi-equilibria in markets with non-convex preferences. Econometrica 37: 25–38.

    Article  Google Scholar 

  • Starrett, D.A. 1971. A note on externalities and the core. Econometrica 41: 179–183.

    Article  Google Scholar 

  • Starrett, D.A. 1972. Fundamental nonconvexities in the theory of externalities. Journal of Economic Theory 4: 180–199.

    Article  Google Scholar 

  • Sun, Y.N. 1999. The complete removal of individual uncertainty: Multiple optimal choices and random economies. Economic Theory 14: 507–544.

    Article  Google Scholar 

  • Sun, Y.N. 2006. The exact law of large numbers via Fubini extension and the characterization of insurable risks. Journal of Economic Theory 126: 31–69.

    Article  Google Scholar 

  • Sun, Y.N., and N.C. Yannelis. 2007a. Perfect competition in asymmetric information economies: Compatibility of efficiency and incentives. Journal of Economic Theory 134: 175–194.

    Article  Google Scholar 

  • Sun, Y.N., and N.C. Yannelis. 2007b. Core, equilibria and incentives in large asymmetric information economies. Games and Economic Behavior 61 (1): 131–155.

    Article  Google Scholar 

  • Tourky, R., and N.C. Yannelis. 2001. Markets with many more agents than commodities: Aumann’s hidden assumption. Journal of Economic Theory 101: 189–221.

    Article  Google Scholar 

  • Trockel, W. 1984. Market demand: An analysis of large economies with nonconvex preferences. Berlin: Springer.

    Book  Google Scholar 

  • Vind, K. 1964. Edgeworth-allocations in an exchange economy with many traders. International Economic Review 5: 165–177.

    Article  Google Scholar 

  • Vohra, R. 1992. Marginal cost pricing under bounded marginal returns. Econometrica 60: 859–876.

    Article  Google Scholar 

  • Weintraub, E.R. 1985. General equilibrium analysis: Studies in appraisal. Cambridge: Cambridge University Press.

    Google Scholar 

  • Winter, E., and M.H. Wooders. 1994. An axiomatization of the core for finite and continuum games. Social Choice and Welfare 11: 165–175.

    Article  Google Scholar 

  • Wooders, M.H. 1997. Equivalence of Lindahl equilibrium with participation prices and the core: An axiomatization of the core for finite and continuum games. Economic Theory 9: 115–127.

    Article  Google Scholar 

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Ali Khan, M. (2018). Perfect Competition. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1633

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