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The Long Run Outcomes And Global Dynamics Of A Duopoly Game With Misspecified Demand Functions

Author

Listed:
  • GIAN-ITALO BISCHI

    () (Istituto di Scienze Economiche, University of Urbino, via Saffi n.42, I-61029 Urbino, Italy)

  • CARL CHIARELLA

    () (School of Finance and Economics, University of Technology Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

  • MICHAEL KOPEL

    () (Department of Managerial Economics and Industrial Organization, University of Technology, Theresianumgasse 27, A-1040 Vienna, Austria)

Abstract

In this paper we study a model of a quantity-setting duopoly market where firms lack knowledge of the market demand. Using a misspecified demand function firms determine their profit-maximizing choices of their corresponding perceived market game. For illustrative purposes we assume that the (true) demand function is linear and that the reaction functions of the players are quadratic. We then investigate the global dynamics of this game and characterize the number of steady states and their welfare properties. We study the basins of attraction of these steady states and present situations in which global bifurcations of their basins occur when model parameters are varied. The economic significance of our result is to show that in situations where players choose their actions based on a misspecified model of the environment, additional self-confirming steady states may emerge, despite the fact that the Nash-equilibrium of the game under perfect knowledge is unique. As a consequence the long run outcome of the game and overall welfare is highly dependent upon initial conditions.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:03:n:s0219198904000253
    DOI: 10.1142/S0219198904000253
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
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    Cited by:

    1. 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.
    2. repec:eee:dyncon:v:91:y:2018:i:c:p:84-103 is not listed on IDEAS
    3. Ruben van de Geer & Arnoud V. den Boer & Christopher Bayliss & Christine Currie & Andria Ellina & Malte Esders & Alwin Haensel & Xiao Lei & Kyle D. S. Maclean & Antonio Martinez-Sykora & Asbj{o}rn Nil, 2018. "Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference," Papers 1804.03219, arXiv.org.

    More about this item

    Keywords

    Oligopoly games; bounded rationality; bifurcations; misspecified demand (function); self-confirming steady states;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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