Skip to main content

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 442))

  • 68 Accesses

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • ARNOLD, V.I.. (1973). Ordinary Differential Equations, MIT Press, Cambridge.

    Google Scholar 

  • ARROW, K., HAHN, F. H. (1971). General Competitive Analysis. Holden Day, S. Francisco.

    Google Scholar 

  • ARROW, K, HURWICZ, L, UZAWA, H. (eds.), (1958). Studies in Linear and Non Linear Programming. Stanford University Press, Stanford, California.

    Google Scholar 

  • BAMON, R, FRAYSSE, J. (1985). “Existence of Cournot Equilibrium in Large Markets”, Econometrica, 53, pp. 587–597.

    Article  Google Scholar 

  • BAUMOL, W.J. (1959). Business Behavior, Value and Growth. McMillan. New York.

    Google Scholar 

  • BARTLE, R.G. (1976). The Elements of Real Analysis, second edition, Wiley and Sons, New York.

    Google Scholar 

  • 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.

    Google Scholar 

  • BOLDRIN, M., MONTRUCCHIO, L (1986). “On the Indeterminacy of Capital Accumulation Paths”. Journal of Economic Theory, 40, n. 1, pp. 26–39.

    Article  Google Scholar 

  • BULOW, J., GEANAKOPLOS, J., KLEMPERER, P. (1985). “Multimarket Oligopoly: Strategic Substitutes and Complements”. Journal of Political Economy, 93, pp. 488–511.

    Article  Google Scholar 

  • DEBREU, G. (1974). “Excess Demand Functions”. Journal of Mathematical Economics 1, pp. 15–21.

    Article  Google Scholar 

  • CAPLIN, A., NALEBUFF, B. (1991). “Aggregation and Imperfect Competition: On the Existence of Equilibrium”, Econometrica 59, pp. 25–29.

    Article  Google Scholar 

  • CARLTON, D. W., and PERLOFF, J. M. (1990). Modern Industrial Organization. Harper-Collins.

    Google Scholar 

  • CORCHON, L. (1994). “Comparative Statics for Aggregative Games: The Strong Concavity Case”, Mathematical Social Sciences, 28, pp. 151–165.

    Article  Google Scholar 

  • 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).

    Google Scholar 

  • COURNOT, A.A. (1838) Recherches sur les Principles Mathematiques de la Thèory del Richesses Hachette, Paris.

    Google Scholar 

  • DANA, R.A., MONTRUCCHIO, L. (1986). “Dynamic Complexity in Duopoly Games”. Journal of Economic Theory, 40, n. 1, pp. 40–56.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • DASGUPTA, P., HEAL, G. (1979). Economic Theory and Exhaustible Resources. Cambridge Economics Handbooks, Cambridge University Press.

    Google Scholar 

  • DIERICKX, I., MATUTES, C., NEVEN, D. (1988). “Indirect Taxation and Cournot Equilibrium”, International Journal of Industrial Organization, 6 pp. 385–399.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • DORFMAN, R., STEINER, P.O. (1954). “Optimal Advertising and Optimal Quality”, American Economic Review, vol. 44, n. 5, pp. 826–836.

    Google Scholar 

  • DUBEY, P., MAS-COLELL, A., SHUBIK, M. (1980). “Efficiency Properties of Strategic Market Games”, Journal of Economic Theory, pp. 339–362.

    Google Scholar 

  • FERSHTMAN, C. (1990) “The Interdependence between Ownership Status and Market Structure: The Case of Privatization”, Economica, 57 pp. 319–328.

    Article  Google Scholar 

  • FRIEDMAN, J. (1977). Oligopoly and the Theory of Games. North Holland. Amsterdam, New York and Oxford.

    Google Scholar 

  • FRIEDMAN, J. (1982). “Oligopoly Theory” in K. Arrow and M. Intrilligator (eds.) Handbook of Mathematical Economics, chp. 11. North Holland. Amsterdam.

    Google Scholar 

  • FRIEDMAN, J. (1983). Oligopoly Theory. Cambridge Surveys of Economic Literature. Cambridge University Press.

    Book  Google Scholar 

  • GAUNERSDORFER, A., HOFBAUER, J. (1994). “Fictitious Play, Shapley Polygons and the Replicator Equation”. Mimeo, Vienna.

    Google Scholar 

  • GROSSMAN, S. (1981). “Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs”. Econometrica, 49, pp. 1149–1172.

    Article  Google Scholar 

  • GUCKENHEIMER, J., HOLMES, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, vol. 42. Springer-Verlag.

    Google Scholar 

  • HAHN, F. (1962). “The Stability of Cournot Oligopoly Solution”. Review of Economic Studies, 29 (4), pp. 329–333.

    Article  Google Scholar 

  • HIRCH, M. SMALE, S. (1974). Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York.

    Google Scholar 

  • HOLDEN, A. V. (1986) (ed.). Chaos. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • HOROWITZ, I. (1987). “Regression-Estimated Market Demand and Quasi-Cournot Behavior”, International Journal of Industrial Organization, 5, pp. 247–253.

    Article  Google Scholar 

  • JACQUEMIN, A., SLADE, M. (1989). “Cartels, collusion and Horizontal Merger” in: Handbook of Industrial Organization ed. by R. Schmalensee and R. Willig. North Holland.

    Google Scholar 

  • KEENAN, D., RADER, T. (1985). “Market Dynamics and the Law of Demand”. Econometrica 53 (2), pp. 465–71.

    Article  Google Scholar 

  • KUKUSHKIN, N.S. (1994). “A Fixed-Point Theorem for Decreasing Mappings”, Economics Letters, 46, pp. 23–26.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • LEFSCHETZ, S. (1946). Lectures on Differential Equations. Princeton University Press.

    Google Scholar 

  • LOURY, G. (1979). “Market Structure and Innovation: A Reformulation”, Quarterly Journal of Economics, No. 93 (3), pp. 395–409.

    Google Scholar 

  • MC MANUS, M. (1962). “Numbers and Size in Cournot Oligopoly”, Yorkshire Bull, 14, pp. 14–22.

    Article  Google Scholar 

  • MC MANUS, M. (1964). “Equilibrium, Numbers and Size in Cournot Oligopoly”, Yorkshire Bull, 16, pp. 68–75.

    Article  Google Scholar 

  • MANTEL, R. (1972). “On the Characterization of Aggregate Excess Demand”. Journal of Economic Theory. 7, pp. 348–53.

    Article  Google Scholar 

  • MARSDEN, J.E., McCRACKEN, M. (1976). The Hopf Bifurcation and Applications. Applied Mathematical Sciences, vol. 19. Springer-Verlag.

    Google Scholar 

  • MASKIN, E., TIROLE, J. (1987). “A Theory of Dynamic Oligopoly III”. European Economic Review, 31, 1987, pp. 947–968.

    Article  Google Scholar 

  • MILGROM, P., ROBERTS, J. (1990). “Rationalizability, Learning and Equilibrium in Games with Strategic Complementarities”, Econometrica 58, n° 6, pp. 1255–1277.

    Google Scholar 

  • MILGROM, P., ROBERTS, J. (1991). “Adaptive and Sophisticated Learning in Normal Form Games” Games and Economic Behavior, pp. 82–100.

    Google Scholar 

  • MOULIN, H. (1986). Game Theory for the Social Sciences (2nd ed.). New York University Press and Columbia University Press. New York.

    Google Scholar 

  • NEGISHI, T. (1961). “Monopolistic Competition and General Equilibrium”. Review of Economic Studies, 28, pp. 196–201.

    Google Scholar 

  • NOVSHEK, W. (1985). “On the Existence of Cournot Equilibrium”. Review of Economic Studies, 52, pp. 85–98.

    Google Scholar 

  • OKUGUCHI, K. (1964). “The Stability of the Cournot Oligopoly Solution: A Further Generalization”. Review of Economic Studies 31 (2), pp. 143–6.

    Article  Google Scholar 

  • OKUGUCHI, K. (1987). “Equilibrium Price in the Bertrand and Cournot Oligopolies”, Journal of Economic Theory, vol. 42 pp. 128–39.

    Article  Google Scholar 

  • ROBERTS, J. and SONNENSCHEIN, H. (1977) “On the Foundations of the Theory of Monopolistic Competition”. Econometrica, 45, pp. 101–113.

    Google Scholar 

  • ROMANO, R. (1988). “Oligopolistic Competition for Market Share Via Voluntary Excess Supply” International Journal of Industrial Organization, pp. 447–468.

    Google Scholar 

  • SALOP S. ET ALIA (1987). “Symposium on Mergers and Antitrust”. Journal of Economic Perspectives, 1. pp. 3–54.

    Google Scholar 

  • 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.

    Google Scholar 

  • SHUBIK, M. (1984). Game Theory in the Social Sciences: Concepts and Solutions. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • SONNENSCHEIN, H. (1972). “Market Excess Demand Functions”. Econometrica 40, 1972, pp. 549–563.

    Article  Google Scholar 

  • TAKAYAMA, A. (1974) Mathematical Economics. The Dryden Press, Hindsdale, Illinois.

    Google Scholar 

  • TOPKIS, D. (1979). “Equilibrium Points in Nonzero-Sum n-Person Submodular Games”. SIAM Journal of Control and Optimization, 17, pp. 773–787.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • VANEK, J. (1975). Self-Management: Economic Liberation of Man. Penguin Books.

    Google Scholar 

  • VICKERS, J. (1985). “Delegation and the Theory of the Firm”, Economic Journal Supplement pp. 138–147.

    Google Scholar 

  • VIVES, X. (1985). “On the Efficiency of Cournot and Bertrand Equilibria with Product Differentiation”. Journal of Economic Theory, 38, 1. June, pp. 166–175.

    Google Scholar 

  • VIVES, X. (1990). “Nash Equilibrium with Strategic Complementarities” Journal of Mathematical Economics, 19 pp. 305–321.

    Google Scholar 

  • YARROW, G.K. (1985). “Welfare Losses in Oligopoly and Monopolistic Competition”, The Journal of Industrial Economics, vol XXXIII, No 4, pp. 515–529.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Publish with us

Policies and ethics