TY - JOUR
T1 - The robustness of a Nash equilibrium simulation model
T2 - Game-theoretic approach using variable metric projection method
AU - Aiyoshi, Eitaro
AU - Maki, Atsushi
AU - Okamoto, Takashi
N1 - Funding Information:
The authors are grateful to Michael McAleer, Les Oxley and the participants at the International Congress on Modelling and Simulation (MODSIM) for helpful comments and suggestions. The second author wishes to acknowledge the financial support of the JSPS Research Grant-in-Aid No. 19530187 .
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/3
Y1 - 2011/3
N2 - 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.
AB - 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.
KW - Nash equilibrium
KW - Oligopoly
KW - Replicator dynamics
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U2 - 10.1016/j.matcom.2010.06.002
DO - 10.1016/j.matcom.2010.06.002
M3 - Article
AN - SCOPUS:79951813103
SN - 0378-4754
VL - 81
SP - 1518
EP - 1526
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
IS - 7
ER -