In considering economic dynamics, it has been known that time delays are inherent in economic phenomena and could be crucial sources for oscillatory behavior. The main aim of this study is to shed light on what effects the delays can generate. To this end, different models of Cournot duopoly with different delays are built in a continuous time framework and their local and global dynamics are analytically and numerically examined. Three major findings are obtained. First, the stability switching conditions are analytically constructed. Second, it is numerically demonstrated that different lengths of the delays are sources for the birth of simple and complicated dynamics. Third, the delay for collecting information on the competitors’ output alone does not affect stability.
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HR considers the case where the delay in the own output of firm is the same as the delays in its competitors, for We adopt the same assumption in the following.
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However, only some parts of the curves are illustrated for graphical simplicity.
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This justification for Model II is suggested by a referee.
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To do output adjustment in system (25), the firms do not need the current output values and the derivatives and The following method can be used. Rewrite the equations as and integrating both sides in interval showing that to obtain only delayed output values are needed. In the more general case of equations numerical methods such as the Euler method, any higher order Runge-Kutta type or linear multistep method can be used, which gives the output values, with a step size and at each step only earlier output values are used. For example, in the case of the Euler method, the recursive relation is given as follows, for Here, and have to be integer multiples of , otherwise the values of and are obtained by interpolation. Bischi et al.8 introduced this general output adjusting form with sign-preserving speeds of adjustments.
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2018
Author(s)
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