Chaotic dynamics in nonlinear duopoly game with heterogeneous players

Agiza, H.N.; Elsadany, A. A.

doi:10.1016/s0096-3003(03)00190-5

Cited by 205 publications

(115 citation statements)

References 14 publications

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“…Agiza and Elsadany [16] built a nonlinear discrete-time duopoly game assuming the oligarchies have heterogeneous expectations. With the discussion of a 6-dimension dynamical system, Ma and Wu [17] described a triopoly game with two products.…”

Section: Literature Reviewmentioning

confidence: 99%

Research on a Triopoly Dynamic Game with Free Market and Bundling Market in the Chinese Telecom Industry

Lou

2018

Discrete Dynamics in Nature and Society

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Based on the real situation of telecom industry in China, we establish a triopoly game model, which includes two competitive telecom firms and their correlative corporation which produces the complementary product. Both free market and bundling market will be concerned in this dynamic model. Moreover, we consider a one-to-many bundling way instead of two complementary products in terms of the proportion of one to one in a bundling product. By numerical simulation, we find that stable space will decrease and decision chaos appears when the degree of the competition becomes fierce between the two competitive telecom firms. Besides, increasing the amount of bundling services provided by a telecom firm can lead to different impacts on the prices of the three firms investigated. This paper enriches the decision-making for the strategy of bundling pricing and will be valuable for the telecom operators.

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Section: Literature Reviewmentioning

confidence: 99%

Research on a Triopoly Dynamic Game with Free Market and Bundling Market in the Chinese Telecom Industry

Lou

2018

Discrete Dynamics in Nature and Society

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“…Another duopoly game model was studied by Bischi et al [11], where firms of naive expectations decided their outputs based 2 Complexity on the reaction functions. Such model was then improved by Agiza and Elsadany [12] to include two heterogeneous players: adaptive expectation player and bounded rational one. More improvements have been conducted in such model by Zhang et al [13] based on considering nonlinear cost functions.…”

Section: Introductionmentioning

confidence: 99%

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

2018

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This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm's preference is represented by a utility function that is derived from a constant elasticity of substitution (CES) production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations.

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“…In the past, a large number of literatures did the research on dynamic behavior of Cournot and Bertrand game, such as A.A. Elsadany [3], Xiaolong Zhu [4], H. N. Agiza [5], A. K. Naimzada [6], Jixiang Zhang [7], Luciano Fanti [8], Baogui Xin [9] and so on, which involved several adjustment rules: naïve [8,10,11], adaptive [5,12], bounded rational [3,4,7,13,14] and local monopolistic approximation [3,14]. Basically, research results of all these papers show that bifurcation and chaos exist in the dynamic system of Cournot and Bertrand game [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Chaotic dynamics in Bertrand model with technological innovation

Wang¹,

Wang²,

Xie³

2017

Vib. proced.

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Abstract. In this paper, the dynamics of a Bertrand duopoly game with technology innovation have been studied, which contains boundedly rational and naive players. They have been analyzed that the stability of the equilibrium point, the bifurcation and chaotic behavior of the dynamic system. It has been proved that technology innovation has played a very important role in the stability of Nash equilibrium point. Technology innovation can enlarge the stability region of the speed and control the chaos of the dynamic system effectively.

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Chaotic dynamics in nonlinear duopoly game with heterogeneous players

Cited by 205 publications

References 14 publications

Research on a Triopoly Dynamic Game with Free Market and Bundling Market in the Chinese Telecom Industry

Research on a Triopoly Dynamic Game with Free Market and Bundling Market in the Chinese Telecom Industry

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Chaotic dynamics in Bertrand model with technological innovation

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