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Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality

机译：具有有限理性的双头垄断Stackelberg博弈模型的复杂动力学分析

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摘要

In view of the effect of differences between plan products and actual products, a duopoly Stackelberg model of competition on output is formulated. The firms announce plan products sequentially in planning phase and act simultaneously in production phase. Backward induction is used to solve subgame Nash equilibrium. The equilibrium outputs and equilibrium profits are affected by cost coefficients. For the duopoly Stackelberg model, a nonlinear dynamical system which describes the time evolution with bounded rationality is analyzed. The equilibria of the corresponding discrete dynamical systems are investigated. The local stability analysis has been carried out The stability of Nash equilibrium gives rise to complex dynamics as some parameters of the model are varied. Numerical simulations were used to show bifurcation diagram, stability region and chaos. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos. (C) 2015 Elsevier Inc. All rights reserved.
机译：针对计划产品与实际产品之间差异的影响，建立了双寡头Stackelberg竞争对产出的模型。这些公司在计划阶段依次宣布计划产品，并在生产阶段同时采取行动。向后归纳法用于解决子博弈纳什均衡。均衡产出和均衡利润受成本系数影响。对于双寡头Stackelberg模型，分析了描述有限理性的时间演化的非线性动力学系统。研究了相应离散动力系统的平衡。进行了局部稳定性分析。随着模型某些参数的变化，纳什平衡的稳定性引起了复杂的动力学。数值模拟用于显示分叉图，稳定区域和混沌。还表明，状态变量反馈和参数变化方法可用于防止系统不稳定和混乱。 （C）2015 Elsevier Inc.保留所有权利。

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