IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v91y2018icp120-133.html
   My bibliography  Save this article

Dynamic analysis of discontinuous best response with innovation

Author

Listed:
  • Lamantia, Fabio
  • Pezzino, Mario
  • Tramontana, Fabio

Abstract

Starting from the static analysis in Eckert et al. (2017), we study a Cournot duopoly where firms can decide to incur fixed costs in activities that improve their competitiveness (i.e. product development or process innovation). Innovation costs generate discontinuities in the firms quantity best response functions and, in turn, a variety of equilibrium configurations, including multiple equilibria. We provide a dynamic global analysis of the equilibria and show the way in which firms’ initial expectations regarding the rivals level of output are crucial in defining the configuration of the long run equilibrium.

Suggested Citation

  • Lamantia, Fabio & Pezzino, Mario & Tramontana, Fabio, 2018. "Dynamic analysis of discontinuous best response with innovation," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 120-133.
    • Handle: RePEc:eee:dyncon:v:91:y:2018:i:c:p:120-133
    DOI: 10.1016/j.jedc.2018.01.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188918300447
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2018.01.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. David Encaoua & Abraham Hollander, 2002. "Competition Policy and Innovation," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 18(1), pages 63-79, Spring.
    3. Marimon, Ramon & Sunder, Shyam, 1994. "Expectations and Learning under Alternative Monetary Regimes: An Experimental Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 131-162, January.
    4. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
    5. Fabio Tramontana & Laura Gardini & T?nu Puu, 2010. "Mathematical Properties of a Combined Cournot-Stackelberg model," Working Papers 1007, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2010.
    6. Dixit, Avinash, 1980. "The Role of Investment in Entry-Deterrence," Economic Journal, Royal Economic Society, vol. 90(357), pages 95-106, March.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    8. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January.
    9. Zhao, Jijun & Szidarovszky, Ferenc, 2008. "N-firm oligopolies with production adjustment costs: Best responses and equilibrium," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 87-99, October.
    10. Marimon, Ramon & Sunder, Shyam, 1993. "Indeterminacy of Equilibria in a Hyperinflationary World: Experimental Evidence," Econometrica, Econometric Society, vol. 61(5), pages 1073-1107, September.
    11. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    12. Bulow, Jeremy & Geanakoplos, John & Klemperer, Paul, 1985. "Holding Idle Capacity to Deter Entry [The Role of Investment in Entry Deterrence]," Economic Journal, Royal Economic Society, vol. 95(377), pages 178-182, March.
    13. Joseph Farrell & Michael L. Katz, 2005. "Competition Or Predation? Consumer Coordination, Strategic Pricing And Price Floors In Network Markets," Journal of Industrial Economics, Wiley Blackwell, vol. 53(2), pages 203-231, June.
    14. David S. Evans & Richard Schmalensee, 2002. "Some Economic Aspects of Antitrust Analysis in Dynamically Competitive Industries," NBER Chapters, in: Innovation Policy and the Economy, Volume 2, pages 1-50, National Bureau of Economic Research, Inc.
    15. Ware, Roger, 1984. "Sunk Costs and Strategic Commitment: A Proposed Three-Stage Equilibrium," Economic Journal, Royal Economic Society, vol. 94(374), pages 370-378, June.
    16. Dawid, Herbert & Kopel, Michael & Kort, Peter M., 2013. "New product introduction and capacity investment by incumbents: Effects of size on strategy," European Journal of Operational Research, Elsevier, vol. 230(1), pages 133-142.
    17. Andrew Eckert & Tilman Klumpp & Xuejuan Su, 2017. "An Equilibrium Selection Theory of Monopolization," Southern Economic Journal, John Wiley & Sons, vol. 83(4), pages 1012-1037, April.
    18. James A. Brander & Barbara J. Spencer, 1983. "Strategic Commitment with R&D: The Symmetric Case," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 225-235, Spring.
    19. Greg Shaffer & Stephen W. Salant, 1999. "Unequal Treatment of Identical Agents in Cournot Equilibrium," American Economic Review, American Economic Association, vol. 89(3), pages 585-604, June.
    20. Bischi Gian Italo & Lamantia Fabio, 2012. "Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    21. Chiarella, Carl & Szidarovszky, Ferenc, 2004. "Dynamic oligopolies without full information and with continuously distributed time lags," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 495-511, August.
    22. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.
    23. Agliari, Anna & Chiarella, Carl & Gardini, Laura, 2006. "A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 60(4), pages 526-552, August.
    24. Dawid, Herbert & Kopel, Michael & Kort, Peter M., 2010. "Innovation threats and strategic responses in oligopoly markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 203-222, August.
    25. Gian-Italo Bischi & Carl Chiarella & Michael Kopel, 2004. "The Long Run Outcomes And Global Dynamics Of A Duopoly Game With Misspecified Demand Functions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 343-379.
    26. Ferenc Szidarovszky & Akio Matsumoto, 2016. "On a Discontinuous Cournot Oligopoly," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 101-118, Springer.
    27. Roberto Cellini & Fabio Lamantia, 2015. "Quality competition in markets with regulated prices and minimum quality standards," Journal of Evolutionary Economics, Springer, vol. 25(2), pages 345-370, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lamantia, Fabio & Pezzino, Mario & Scardamaglia, Bruno & Tramontana, Fabio, 2022. "A discontinuous model of duopoly with isoelastic demand and innovation costs," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    2. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    3. Michael Kopel & Clemens Löffler, 2008. "Commitment, first-mover-, and second-mover advantage," Journal of Economics, Springer, vol. 94(2), pages 143-166, July.
    4. Andrew Eckert & Tilman Klumpp & Xuejuan Su, 2017. "An Equilibrium Selection Theory of Monopolization," Southern Economic Journal, John Wiley & Sons, vol. 83(4), pages 1012-1037, April.
    5. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, vol. 15(3), pages 349-368, May.
    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. Michael Waldman, 1987. "Underinvestment in Entry Deterrence: When and Why," UCLA Economics Working Papers 456, UCLA Department of Economics.
    8. Ino, Hiroaki & Matsueda, Norimichi & Matsumura, Toshihiro, 2022. "Market competition and strategic choices of electric power sources under fluctuating demand," Resource and Energy Economics, Elsevier, vol. 68(C).
    9. Dawid, Herbert & Kopel, Michael & Kort, Peter M., 2013. "New product introduction and capacity investment by incumbents: Effects of size on strategy," European Journal of Operational Research, Elsevier, vol. 230(1), pages 133-142.
    10. 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.
    11. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    12. Ohnishi, Kazuhiro, 2019. "Capacity choice in an international mixed triopoly," MPRA Paper 94051, University Library of Munich, Germany.
    13. Meunier, Guy, 2008. "Strategic commitment in a mixed oligopoly," Research in Economics, Elsevier, vol. 62(2), pages 92-100, June.
    14. Felix Munoz-Garcia & Gulnara Zaynutdinova, 2013. "Capacity Constrained Firms and Expansion Subsidies: Should Governments Avoid Generous Subsidies?," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 563-597, December.
    15. Antoci, Angelo & Gay, Antonio & Landi, Massimiliano & Sacco, Pier Luigi, 2008. "Global analysis of an expectations augmented evolutionary dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3877-3894, December.
    16. S H Martzoukos, 2009. "Real R&D options and optimal activation of two-dimensional random controls," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 843-858, June.
    17. Luciano Fanti & Nicola Meccheri, 2014. "Capacity choice and welfare under alternative unionisation structures," Discussion Papers 2014/176, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    18. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 376-408, June.
    19. Kazuhiro Ohnishi, 2022. "Lifetime Employment and Stackelberg Mixed Duopoly Games with a Foreign Labour-Managed Competitor," Arthaniti: Journal of Economic Theory and Practice, , vol. 21(1), pages 27-42, June.
    20. Ravi Kumar, K. & Hadjinicola, George C., 1996. "Resource allocation to defensive marketing and manufacturing strategies," European Journal of Operational Research, Elsevier, vol. 94(3), pages 453-466, November.

    More about this item

    Keywords

    Process innovation; Oligopolistic competition; Discontinuous best response functions; Global analysis; Learning;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:91:y:2018:i:c:p:120-133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.