Abstract
Games and Aggregative Games. Characterization of Games with Strategic Substitutes (Proposition 1.1). Existence (Proposition 1.2), Uniqueness (Proposition 1.3), Inefficiency (Proposition 1.4) and Stability (Propositions 1.5–6) of Nash Equilibrium in Aggregative Games with Strategic Substitutes. Characterization of Games with Strategic Complements (Proposition 1.7). Existence (Proposition 1.8), Uniqueness (Proposition 1.9), Inefficiency (Proposition 1.10) and Stability (Proposition 1.11) of Nash Equilibrium in Games with Strategic Complements. Appendix: Further Results on the Stability of Equilibrium (Propositions 1.12–14).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ARNOLD, V.I.. (1973). Ordinary Differential Equations, MIT Press, Cambridge.
ARROW, K., HAHN, F. H. (1971). General Competitive Analysis. Holden Day, S. Francisco.
ARROW, K, HURWICZ, L, UZAWA, H. (eds.), (1958). Studies in Linear and Non Linear Programming. Stanford University Press, Stanford, California.
BAMON, R, FRAYSSE, J. (1985). “Existence of Cournot Equilibrium in Large Markets”, Econometrica, 53, pp. 587–597.
BAUMOL, W.J. (1959). Business Behavior, Value and Growth. McMillan. New York.
BARTLE, R.G. (1976). The Elements of Real Analysis, second edition, Wiley and Sons, New York.
BERTRAND, J. (1883). “Review of ”Theorie Matematique de la Richesse Social“ and ”Recherches sur les Principles Mathematiques de la Thèory del Richesses“. Journal des Savants, pp. 499–508.
BOLDRIN, M., MONTRUCCHIO, L (1986). “On the Indeterminacy of Capital Accumulation Paths”. Journal of Economic Theory, 40, n. 1, pp. 26–39.
BULOW, J., GEANAKOPLOS, J., KLEMPERER, P. (1985). “Multimarket Oligopoly: Strategic Substitutes and Complements”. Journal of Political Economy, 93, pp. 488–511.
DEBREU, G. (1974). “Excess Demand Functions”. Journal of Mathematical Economics 1, pp. 15–21.
CAPLIN, A., NALEBUFF, B. (1991). “Aggregation and Imperfect Competition: On the Existence of Equilibrium”, Econometrica 59, pp. 25–29.
CARLTON, D. W., and PERLOFF, J. M. (1990). Modern Industrial Organization. Harper-Collins.
CORCHON, L. (1994). “Comparative Statics for Aggregative Games: The Strong Concavity Case”, Mathematical Social Sciences, 28, pp. 151–165.
CORCHON, L., MAS-COLELL, A. (1995). “A Note on Stability of Best Reply and Gradient Systems with Applications to Imperfectly Competitive Models”. Economics Letters (forthcoming).
COURNOT, A.A. (1838) Recherches sur les Principles Mathematiques de la Thèory del Richesses Hachette, Paris.
DANA, R.A., MONTRUCCHIO, L. (1986). “Dynamic Complexity in Duopoly Games”. Journal of Economic Theory, 40, n. 1, pp. 40–56.
DANA, R.A., MONTRUCCHIO, L. (1987). “On Rational Dynamic Strategies in Infinite Horizon Models where Agents Discount the Future”. Journal of Economic Behavior and Organization, 8, pp. 497–511.
DASGUPTA, P., HEAL, G. (1979). Economic Theory and Exhaustible Resources. Cambridge Economics Handbooks, Cambridge University Press.
DIERICKX, I., MATUTES, C., NEVEN, D. (1988). “Indirect Taxation and Cournot Equilibrium”, International Journal of Industrial Organization, 6 pp. 385–399.
DIERKER, E. (1991) “Competition for Customers” in Barnett et alia (eds.) Equilibrium Theory and Applications: Proceedings of the Sixth International Symposium in Economic Theory and Econometrics. Cambridge University Press, Cambridge, pp. 383–402.
DORFMAN, R., STEINER, P.O. (1954). “Optimal Advertising and Optimal Quality”, American Economic Review, vol. 44, n. 5, pp. 826–836.
DUBEY, P., MAS-COLELL, A., SHUBIK, M. (1980). “Efficiency Properties of Strategic Market Games”, Journal of Economic Theory, pp. 339–362.
FERSHTMAN, C. (1990) “The Interdependence between Ownership Status and Market Structure: The Case of Privatization”, Economica, 57 pp. 319–328.
FRIEDMAN, J. (1977). Oligopoly and the Theory of Games. North Holland. Amsterdam, New York and Oxford.
FRIEDMAN, J. (1982). “Oligopoly Theory” in K. Arrow and M. Intrilligator (eds.) Handbook of Mathematical Economics, chp. 11. North Holland. Amsterdam.
FRIEDMAN, J. (1983). Oligopoly Theory. Cambridge Surveys of Economic Literature. Cambridge University Press.
GAUNERSDORFER, A., HOFBAUER, J. (1994). “Fictitious Play, Shapley Polygons and the Replicator Equation”. Mimeo, Vienna.
GROSSMAN, S. (1981). “Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs”. Econometrica, 49, pp. 1149–1172.
GUCKENHEIMER, J., HOLMES, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, vol. 42. Springer-Verlag.
HAHN, F. (1962). “The Stability of Cournot Oligopoly Solution”. Review of Economic Studies, 29 (4), pp. 329–333.
HIRCH, M. SMALE, S. (1974). Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York.
HOLDEN, A. V. (1986) (ed.). Chaos. Princeton University Press, Princeton, New Jersey.
HOROWITZ, I. (1987). “Regression-Estimated Market Demand and Quasi-Cournot Behavior”, International Journal of Industrial Organization, 5, pp. 247–253.
JACQUEMIN, A., SLADE, M. (1989). “Cartels, collusion and Horizontal Merger” in: Handbook of Industrial Organization ed. by R. Schmalensee and R. Willig. North Holland.
KEENAN, D., RADER, T. (1985). “Market Dynamics and the Law of Demand”. Econometrica 53 (2), pp. 465–71.
KUKUSHKIN, N.S. (1994). “A Fixed-Point Theorem for Decreasing Mappings”, Economics Letters, 46, pp. 23–26.
LIPPMAN, S.A., MAMER, J.W., MC CARDLE, K.F. (1987). “Comparative Statics in Non-cooperative Games via Transinfmitely Iterated Play”. Journal of Economic Theory 41, pp. 288–303.
LEFSCHETZ, S. (1946). Lectures on Differential Equations. Princeton University Press.
LOURY, G. (1979). “Market Structure and Innovation: A Reformulation”, Quarterly Journal of Economics, No. 93 (3), pp. 395–409.
MC MANUS, M. (1962). “Numbers and Size in Cournot Oligopoly”, Yorkshire Bull, 14, pp. 14–22.
MC MANUS, M. (1964). “Equilibrium, Numbers and Size in Cournot Oligopoly”, Yorkshire Bull, 16, pp. 68–75.
MANTEL, R. (1972). “On the Characterization of Aggregate Excess Demand”. Journal of Economic Theory. 7, pp. 348–53.
MARSDEN, J.E., McCRACKEN, M. (1976). The Hopf Bifurcation and Applications. Applied Mathematical Sciences, vol. 19. Springer-Verlag.
MASKIN, E., TIROLE, J. (1987). “A Theory of Dynamic Oligopoly III”. European Economic Review, 31, 1987, pp. 947–968.
MILGROM, P., ROBERTS, J. (1990). “Rationalizability, Learning and Equilibrium in Games with Strategic Complementarities”, Econometrica 58, n° 6, pp. 1255–1277.
MILGROM, P., ROBERTS, J. (1991). “Adaptive and Sophisticated Learning in Normal Form Games” Games and Economic Behavior, pp. 82–100.
MOULIN, H. (1986). Game Theory for the Social Sciences (2nd ed.). New York University Press and Columbia University Press. New York.
NEGISHI, T. (1961). “Monopolistic Competition and General Equilibrium”. Review of Economic Studies, 28, pp. 196–201.
NOVSHEK, W. (1985). “On the Existence of Cournot Equilibrium”. Review of Economic Studies, 52, pp. 85–98.
OKUGUCHI, K. (1964). “The Stability of the Cournot Oligopoly Solution: A Further Generalization”. Review of Economic Studies 31 (2), pp. 143–6.
OKUGUCHI, K. (1987). “Equilibrium Price in the Bertrand and Cournot Oligopolies”, Journal of Economic Theory, vol. 42 pp. 128–39.
ROBERTS, J. and SONNENSCHEIN, H. (1977) “On the Foundations of the Theory of Monopolistic Competition”. Econometrica, 45, pp. 101–113.
ROMANO, R. (1988). “Oligopolistic Competition for Market Share Via Voluntary Excess Supply” International Journal of Industrial Organization, pp. 447–468.
SALOP S. ET ALIA (1987). “Symposium on Mergers and Antitrust”. Journal of Economic Perspectives, 1. pp. 3–54.
SHAFER, W, SONNENSCHEIN, H. (1982). “Market Demand and Excess Demand Functions” in K. Arrow and M. Intrilligator (eds.) Handbook of Mathematical Economics, chp. 14. North Holland. Amsterdam, New York and Oxford.
SHUBIK, M. (1984). Game Theory in the Social Sciences: Concepts and Solutions. MIT Press, Cambridge, Massachusetts.
SONNENSCHEIN, H. (1972). “Market Excess Demand Functions”. Econometrica 40, 1972, pp. 549–563.
TAKAYAMA, A. (1974) Mathematical Economics. The Dryden Press, Hindsdale, Illinois.
TOPKIS, D. (1979). “Equilibrium Points in Nonzero-Sum n-Person Submodular Games”. SIAM Journal of Control and Optimization, 17, pp. 773–787.
TULLOCK, G. (1980). “Efficient Rent-Seeking” in J.M. Buchanan, R.D. Tollison and G. Tullock (eds) Towards a Theory of a Rent-Seeking Society, Texas A and M University Press, pp. 97–112.
VANEK, J. (1975). Self-Management: Economic Liberation of Man. Penguin Books.
VICKERS, J. (1985). “Delegation and the Theory of the Firm”, Economic Journal Supplement pp. 138–147.
VIVES, X. (1985). “On the Efficiency of Cournot and Bertrand Equilibria with Product Differentiation”. Journal of Economic Theory, 38, 1. June, pp. 166–175.
VIVES, X. (1990). “Nash Equilibrium with Strategic Complementarities” Journal of Mathematical Economics, 19 pp. 305–321.
YARROW, G.K. (1985). “Welfare Losses in Oligopoly and Monopolistic Competition”, The Journal of Industrial Economics, vol XXXIII, No 4, pp. 515–529.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Corchón, L. (1996). Nash Equilibrium. In: Theories of Imperfectly Competitive Markets. Lecture Notes in Economics and Mathematical Systems, vol 442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22531-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-22531-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61553-8
Online ISBN: 978-3-662-22531-8
eBook Packages: Springer Book Archive