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On price stability and the nature of product differentiation

Author

Listed:
  • Joaquín Andaluz

    (University of Zaragoza)

  • Gloria Jarne

    (University of Zaragoza)

Abstract

In a spatial competition model, we analyze the stability of the Nash-price equilibrium under horizontal and vertical product differentiation, considering both homogenous and heterogeneous expectations. Regardless of the nature of product differentiation, assuming that firms behave according to an adaptive expectations rule, it is found that the Nash-price equilibrium is asymptotically stable. If at least one firm follows the gradient rule based on marginal profit, an increase in the adjustment speed turns out to be a source of complexity. Moreover, the influence of the locations on price stability depends on the nature of product differentiation and on the expectations scheme.

Suggested Citation

  • Joaquín Andaluz & Gloria Jarne, 2019. "On price stability and the nature of product differentiation," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 741-762, April.
    • Handle: RePEc:spr:joevec:v:29:y:2019:i:2:d:10.1007_s00191-018-0584-2
    DOI: 10.1007/s00191-018-0584-2
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    1. Gabszewicz, Jean Jaskold & Thisse, Jacques-Francois, 1986. "On the Nature of Competition with Differentiated Products," Economic Journal, Royal Economic Society, vol. 96(381), pages 160-172, March.
    2. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    3. Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-366, May.
    4. Joaquín Andaluz & Gloria Jarne, 2016. "Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational," Annals of Operations Research, Springer, vol. 238(1), pages 1-25, March.
    5. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    6. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    7. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2009. "The dynamics of Bertrand model with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2048-2055.
    8. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    9. Naimzada, A.K. & Tramontana, F., 2012. "Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products," Economic Modelling, Elsevier, vol. 29(4), pages 1436-1439.
    10. S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.
    11. Andaluz, J. & Elsadany, A.A. & Jarne, G., 2017. "Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 86-99.
    12. Matthew Lewis, 2008. "Price Dispersion And Competition With Differentiated Sellers," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 654-678, September.
    13. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    14. Yu, Weisheng & Yu, Yu, 2014. "The complexion of dynamic duopoly game with horizontal differentiated products," Economic Modelling, Elsevier, vol. 41(C), pages 289-297.
    15. Qian Liu & Dan Zhang, 2013. "Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation," Management Science, INFORMS, vol. 59(1), pages 84-101, August.
    16. Tremblay, Carol Horton & Tremblay, Victor J., 2011. "The Cournot-Bertrand model and the degree of product differentiation," Economics Letters, Elsevier, vol. 111(3), pages 233-235, June.
    17. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    18. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    19. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2013. "The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 73-86.
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    More about this item

    Keywords

    Horizontal product differentiation; Vertical product differentiation; Bounded rationality; Dynamic stability;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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