Abstract
In this paper we concern the investment process in a duopoly game played by heterogeneous players. A discrete and dynamic system is built for the case that a boundedly rational player adjusts its investment decision by the locally marginal profit and a naïve player chooses its strategy according to the opponent’s action in the previous period. By stability analysis of the system, we show that the boundary equilibrium is unstable and obtain the stability conditions for the interior equilibrium. Numerical simulations are used to provide evidence for the influence of the model parameters on the system stability and on the complicated behaviors in the system evolution. It is shown that the system with varying model parameters may drive to chaos and the loss of stability may be caused by period doubling bifurcations or Neimark–Sacker bifurcations. It is also shown that the time-delayed feedback control method can be used to keep the system from instability and chaos. All the numerical simulations show that the capital depreciation rate has great influence on the system evolution: a smaller depreciation rate has a stronger stabilization effect on the survival of the system and makes the system easier to control from chaos.
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