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Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

Author

Listed:
  • Giancarlo Bigi

    (Università di Pisa)

  • Mauro Passacantando

    (Università di Pisa)

Abstract

A Nash–Cournot model for oligopolistic markets with concave cost functions and a differentiated commodity is analyzed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity assumptions. The results of some numerical tests on randomly generated markets are also reported.

Suggested Citation

  • Giancarlo Bigi & Mauro Passacantando, 2017. "Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 63-79, November.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0187-7
    DOI: 10.1007/s10203-017-0187-7
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    References listed on IDEAS

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    1. Bonanno, Giacomo, 1990. "General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
    2. Pierre von Mouche & Federico Quartieri (ed.), 2016. "Equilibrium Theory for Cournot Oligopolies and Related Games," Springer Series in Game Theory, Springer, number 978-3-319-29254-0, June.
    3. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    4. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    5. Stephen W. Salant, 1982. "Imperfect Competition in the International Energy Market: A Computerized Nash-Cournot Model," Operations Research, INFORMS, vol. 30(2), pages 252-280, April.
    6. Nagurney, Anna, 1988. "Algorithms for oligopolistic market equilibrium problems," Regional Science and Urban Economics, Elsevier, vol. 18(3), pages 425-445, August.
    7. Charles D. Kolstad & Lars Mathiesen, 1991. "Computing Cournot-Nash Equilibria," Operations Research, INFORMS, vol. 39(5), pages 739-748, October.
    8. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    9. Sjur D. Flåm & Adi Ben-Israel, 1990. "A Continuous Approach to Oligopolistic Market Equilibrium," Operations Research, INFORMS, vol. 38(6), pages 1045-1051, December.
    10. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    11. M. Castellani & M. Giuli, 2010. "On Equivalent Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 157-168, October.
    12. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Vives, Xavier, 1989. "Cournot and the oligopoly problem," European Economic Review, Elsevier, vol. 33(2-3), pages 503-514, March.
    14. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.
    15. I.V. Konnov, 2003. "Application of the Proximal Point Method to Nonmonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 317-333, November.
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