电力和可再生资源市场古诺动态博弈模型及其动力学研究
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摘要
本文首先分别建立了新能源发展背景下的电力市场上的双寡头、三寡头和四寡头古诺动态博弈模型。接着，本文建立了可再生资源市场上的双寡头和三寡头古诺动态博弈模型。通过运用非线性科学中的分岔和混沌理论，结合经济学原理，深入研究了所建立起来的非线性离散动力系统模型的稳定性及其内在复杂性。本文所做的创新性工作主要如下：
1.首先，根据相关文献和电力市场的实际情况，在新能源发展背景下，考虑到电力企业获取信息能力的差异，分别在有限理性、延迟有限理性、信息延迟有限理性下建立了电力市场中的非线性双寡头古诺动态博弈模型。该模型采用平方形式的反需求函数；采用两种不同形式的成本函数，传统煤电企的成本函数是二项式形式的，新能源电企的成本函数是线性形式的。通过理论分析和数值仿真，给出了系统纳什均衡点的局部稳定域。进一步，具体分析了产量调整速度参数对系统的动力学行为的影响。
2.因电力企业的产量决策方式可能不相同，所以它们对未来的预期也可能不一样。本文在不同策略（包括有限理性策略、自适应策略、静态预期策略）组合的条件下，建立了新能源发展背景下电力市场中的三寡头古诺动态博弈模型，研究了产量调整速度对电力市场稳定性的影响及其模型的复杂动力学特征。另外，在有限理性策略下，建立了新能源发展背景下电力市场中的四寡头古诺博弈模型，且具体研究了该模型的稳定性及其内在复杂性。
3.在相关文献的基础上，本文建立了有限理性策略下可再生资源市场中的双寡头和三寡头古诺动态博弈模型，该模型具有线性的反需求函数和非线性的成本函数。具体分析了产量调整速度对可再生资源市场稳定性的影响。
4.另外，考虑到可再生资源企业之间可能存在合作关系，它们之间会建立团体组织。本文分别建立了新的有限理性策略下和团队组合下的可再生资源市场中的双寡头和三寡头古诺动态博弈模型。具体研究了产量调整速度和组合权重对系统的动力学特性的影响。
5.分别利用参数调整法、直线稳定法、延迟反馈控制法、线性反馈控制法对系统的混沌行为进行了有效的控制，使分岔和混沌等复杂现象得以推迟或消除。此外，给出了系统的稳定性、混沌及其控制在经济学上的内涵，对解决经济管理中的实际问题具有重要的理论和实际应用价值。
Based on the the related literatures and the the actual situation of the electricity mar-ket under background of the development of new energy, dynamical Cournot duopolygame models, three oligarchs and the four oligarchs nonlinear dynamical Cournot gamemodels in the electricity market under the background of development of new energy arebuilt up, respectively. Further more, based the related literatures, the nonlinear dynam-ical duopoly and triopoly game models with bounded strategy, and the dynamical teamduopoly and triopoly game models with bounded strategy in the renewable resource mar-ket are established, respectively. By the theory of bifurcation and chaos in the nonlineardynamic science, combining the principles of economics, the stability and the inherentcomplexity of the established models are deeply analyzed and considered.
The innovative contents in this paper are mainly as follows:
1. First of all, according to the related literatures and the actual situation of theelectricity market under background of the development of new energy, three diferen-t nonlinear dynamical Cournot duopoly game models are established, which are underthe strategies of bounded rationality, delay bounded rationality, delay bounded rational-ity because of delayed information. According to the actual situation of the electricitymarket, the models have the square form inverse demand function and two types of costfunctions (the traditional coal companies have binomial form cost functions, but the newenergy companies have linear form cost functions), which are more in accord with theactual situation of the electricity market under background of the development of new en-ergy. By theoretical analysis and numerical simulations, the regions of the local stabilityof the Nash equilibrium points are obtained. Furthermore, the output adjustment speedparameters efect on the dynamic behaviors of the systems, which are analyzed in detail.
2. As the electricity firms may make heterogeneous output strategies, the expec-tations of the electricity firms may diferent. In this paper, under the portfolio strategies(including bounded rationality strategies, adaptive strategies, the static expected strategy),three types of triopoly nonlinear dynamical Cournot game models in the electricity marketunder the background of development of new energy are built up. The output adjustmentspeed parameters efect on the triopoly nonlinear dynamical Cournot game models withdiferent expectation strategies, and the complex dynamic behaviors of the models arestudied in detail. Furthermore, the four oligarchs game model in the in the electricitymarket under the background of development of new energy with bounded rationality strategy is established, and the stability and the inherent complexity of the models arestudied in detail.
3.Based on the related reference literatures, the duopoly and the triopoly dynami-cal Cournot game models in the renewable resources market with bounded rationality areestablished. The models have linear inverse demand functions and nonlinear cost func-tions. Furthermore, the output adjustment speed parameters impact on the stability of therenewable resource market, which are analyzed in detail.
4. Furthermore, as there may be existed collaboration relationship between the re-newable resource enterprises, the oligarch enterprises may establish team organization.The team duopoly and the triopoly with team players dynamical Cournot game modelsin the renewable resources market with bounded rationality are respectively establishedin this paper. The influences of the output adjustment speed parameters and the weightfactor of the team on the dynamic characteristics of the systems are researched in detail.
5. Oligopolistic firms over production competition game may cause the market toinstability, and even lead to a chaotic state.The parameters adjustment, the straight-linestabilization, the time-delayed feedback and the linear feedback methods are used to con-trol of the chaotic behaviors of the systems, which are efciently to postpone or eliminatethe complex phenomenon of bifurcation and chaos. In this paper, the stability of thesystem, chaos and its control are given economic connotations which are provided veryuseful theoretical and practical values to solve problems in economics and management.
1.首先，根据相关文献和电力市场的实际情况，在新能源发展背景下，考虑到电力企业获取信息能力的差异，分别在有限理性、延迟有限理性、信息延迟有限理性下建立了电力市场中的非线性双寡头古诺动态博弈模型。该模型采用平方形式的反需求函数；采用两种不同形式的成本函数，传统煤电企的成本函数是二项式形式的，新能源电企的成本函数是线性形式的。通过理论分析和数值仿真，给出了系统纳什均衡点的局部稳定域。进一步，具体分析了产量调整速度参数对系统的动力学行为的影响。
2.因电力企业的产量决策方式可能不相同，所以它们对未来的预期也可能不一样。本文在不同策略（包括有限理性策略、自适应策略、静态预期策略）组合的条件下，建立了新能源发展背景下电力市场中的三寡头古诺动态博弈模型，研究了产量调整速度对电力市场稳定性的影响及其模型的复杂动力学特征。另外，在有限理性策略下，建立了新能源发展背景下电力市场中的四寡头古诺博弈模型，且具体研究了该模型的稳定性及其内在复杂性。
3.在相关文献的基础上，本文建立了有限理性策略下可再生资源市场中的双寡头和三寡头古诺动态博弈模型，该模型具有线性的反需求函数和非线性的成本函数。具体分析了产量调整速度对可再生资源市场稳定性的影响。
4.另外，考虑到可再生资源企业之间可能存在合作关系，它们之间会建立团体组织。本文分别建立了新的有限理性策略下和团队组合下的可再生资源市场中的双寡头和三寡头古诺动态博弈模型。具体研究了产量调整速度和组合权重对系统的动力学特性的影响。
5.分别利用参数调整法、直线稳定法、延迟反馈控制法、线性反馈控制法对系统的混沌行为进行了有效的控制，使分岔和混沌等复杂现象得以推迟或消除。此外，给出了系统的稳定性、混沌及其控制在经济学上的内涵，对解决经济管理中的实际问题具有重要的理论和实际应用价值。
Based on the the related literatures and the the actual situation of the electricity mar-ket under background of the development of new energy, dynamical Cournot duopolygame models, three oligarchs and the four oligarchs nonlinear dynamical Cournot gamemodels in the electricity market under the background of development of new energy arebuilt up, respectively. Further more, based the related literatures, the nonlinear dynam-ical duopoly and triopoly game models with bounded strategy, and the dynamical teamduopoly and triopoly game models with bounded strategy in the renewable resource mar-ket are established, respectively. By the theory of bifurcation and chaos in the nonlineardynamic science, combining the principles of economics, the stability and the inherentcomplexity of the established models are deeply analyzed and considered.
The innovative contents in this paper are mainly as follows:
1. First of all, according to the related literatures and the actual situation of theelectricity market under background of the development of new energy, three diferen-t nonlinear dynamical Cournot duopoly game models are established, which are underthe strategies of bounded rationality, delay bounded rationality, delay bounded rational-ity because of delayed information. According to the actual situation of the electricitymarket, the models have the square form inverse demand function and two types of costfunctions (the traditional coal companies have binomial form cost functions, but the newenergy companies have linear form cost functions), which are more in accord with theactual situation of the electricity market under background of the development of new en-ergy. By theoretical analysis and numerical simulations, the regions of the local stabilityof the Nash equilibrium points are obtained. Furthermore, the output adjustment speedparameters efect on the dynamic behaviors of the systems, which are analyzed in detail.
2. As the electricity firms may make heterogeneous output strategies, the expec-tations of the electricity firms may diferent. In this paper, under the portfolio strategies(including bounded rationality strategies, adaptive strategies, the static expected strategy),three types of triopoly nonlinear dynamical Cournot game models in the electricity marketunder the background of development of new energy are built up. The output adjustmentspeed parameters efect on the triopoly nonlinear dynamical Cournot game models withdiferent expectation strategies, and the complex dynamic behaviors of the models arestudied in detail. Furthermore, the four oligarchs game model in the in the electricitymarket under the background of development of new energy with bounded rationality strategy is established, and the stability and the inherent complexity of the models arestudied in detail.
3.Based on the related reference literatures, the duopoly and the triopoly dynami-cal Cournot game models in the renewable resources market with bounded rationality areestablished. The models have linear inverse demand functions and nonlinear cost func-tions. Furthermore, the output adjustment speed parameters impact on the stability of therenewable resource market, which are analyzed in detail.
4. Furthermore, as there may be existed collaboration relationship between the re-newable resource enterprises, the oligarch enterprises may establish team organization.The team duopoly and the triopoly with team players dynamical Cournot game modelsin the renewable resources market with bounded rationality are respectively establishedin this paper. The influences of the output adjustment speed parameters and the weightfactor of the team on the dynamic characteristics of the systems are researched in detail.
5. Oligopolistic firms over production competition game may cause the market toinstability, and even lead to a chaotic state.The parameters adjustment, the straight-linestabilization, the time-delayed feedback and the linear feedback methods are used to con-trol of the chaotic behaviors of the systems, which are efciently to postpone or eliminatethe complex phenomenon of bifurcation and chaos. In this paper, the stability of thesystem, chaos and its control are given economic connotations which are provided veryuseful theoretical and practical values to solve problems in economics and management.
引文
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