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The robustness of a Nash equilibrium simulation model: Game-theoretic approach using variable metric projection method

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  • Aiyoshi, Eitaro
  • Maki, Atsushi
  • Okamoto, Takashi

Abstract

This paper proposes a Nash equilibrium model that applies continuous time replicator dynamics to the analysis of oligopoly markets. The robustness of the proposed simple Nash equilibrium model under the simultaneous constraints of allocation of product and market share using a simulation method to derive an optimal solution for production decisions by rival firms in oligopoly markets is tested by changing profit and cost function parameters, as well as the initial production values and market shares of the firms examined in this study. The effects of differences in conjectural variation and initial allocation of market share on the convergent values are considered, particularly in the case of corner solutions. This approach facilitates the understanding of the robustness of attaining equilibrium in an oligopoly market.

Suggested Citation

  • Aiyoshi, Eitaro & Maki, Atsushi & Okamoto, Takashi, 2011. "The robustness of a Nash equilibrium simulation model: Game-theoretic approach using variable metric projection method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1518-1526.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:7:p:1518-1526
    DOI: 10.1016/j.matcom.2010.06.002
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    References listed on IDEAS

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    1. Aiyoshi, Eitaro & Maki, Atsushi, 2009. "A Nash equilibrium solution in an oligopoly market: The search for Nash equilibrium solutions with replicator equations derived from the gradient dynamics of a simplex algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2724-2732.
    2. Klepper, Gernot, 1990. "Entry into the market for large transport aircraft," European Economic Review, Elsevier, vol. 34(4), pages 775-798, June.
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