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Oligopoly Games with Local Monopolistic Approximation

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Author Info

  • Gian-Italo Bischi

    () (University of Urbino)

  • Ahmad K. Naimzada

    () (Department of Economics, University of Milan-Bicocca)

  • Lucia Sbragia

    () (Catholic University of Milan)

Abstract

We propose a repeated oligopoly game where quantity setting firms have incomplete knowledge of the demand function of the market in which they operate. At each time step they solve a profit maximization problem by using a subjective approximation of the demand function based on a local estimate its partial derivative, computed at the current values of prices and outputs, obtained through market experiments. At each time step they extrapolate such local approximation by assuming a linear demand function and ignoring the effects of the competitors outputs. Despite a so rough approximation, that we call "Local Monopolistic Approximation" (LMA), the repeated game may converge to a Nash equilibrium of the true oligopoly game, i.e. the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Sufficient conditions for the local stability of Nash Equilibria are given. In the particular case of an isoelastic demand function, we show that the repeatead game based on LMA always converges to a Nash equilibrium, both with linear and quadratic cost functions. This stability result is compared with "best reply" dynamics, obtained under the assumption of isoelastic demand (fully known by the players) and linear costs.

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File URL: http://dipeco.economia.unimib.it/repec/pdf/mibwpaper81.pdf
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Bibliographic Info

Paper provided by University of Milano-Bicocca, Department of Economics in its series Working Papers with number 81.

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Date of creation: Nov 2004
Date of revision: Nov 2004
Handle: RePEc:mib:wpaper:81

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Related research

Keywords: Oligopoly games; bounded rationality; subjective demand; Nash equilibrium; dynamical systems; stability;

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References

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  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. Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  3. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
  4. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
  5. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
  6. Huang, Weihong, 1995. "Caution implies profit," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 257-277, July.
  7. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  8. Bonanno, Giacomo & Christopher Zeeman, E., 1985. "Limited knowledge of demand and oligopoly equilibria," Journal of Economic Theory, Elsevier, vol. 35(2), pages 276-283, August.
  9. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
  10. Silvestre, Joaquim, 1977. "A model of general equilibrium with monopolistic behavior," Journal of Economic Theory, Elsevier, vol. 16(2), pages 425-442, December.
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Citations

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Cited by:
  1. Ahmad Naimzada & Fabio Tramontana, 2011. "Double route to chaos in an heterogeneous triopoly game," Quaderni di Dipartimento 149, University of Pavia, Department of Economics and Quantitative Methods.
  2. Naimzada, Ahmad & Ricchiuti, Giorgio, 2011. "Monopoly with local knowledge of demand function," Economic Modelling, Elsevier, vol. 28(1-2), pages 299-307, January.
  3. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  4. Arranz Sombría, M. Rosa, 2011. "Cooperación en modelos de Cournot con información incompleta/Cooperation in Cournot’s Models with Incomplete Information," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 397 (18 pá, Abril.
  5. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
  6. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.

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