Global Analysis of a Dynamic Duopoly Game with Bounded Rationality

Bischi, Gian Italo; Naimzada, Ahmad

doi:10.1007/978-1-4612-1336-9_20

Cited by 173 publications

(161 citation statements)

References 15 publications

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“…To give a specific form for dynamics (10), in our model we also assume linear inverse demand function [5,9,10,13,14,18,23,24,26,[32][33][34]:…”

Section: Two Different Delay Structuresmentioning

confidence: 99%

“…Bischi and Naimzada [9] first gave the general formula of bounded rationality in a duopoly game, where each firm uses the local knowledge of its marginal profit to adjust strategy in a new period: increasing its output if it perceives a positive marginal profit and decreasing its production if the perceived marginal profit is negative. A great deal of research work has been done for the dynamical Cournot game played by homogeneous players with such a kind of rationality (e.g., [9][10][11][12]). …”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Duopoly Game with Two Different Delay Structures

Jiang¹,

Xu²,

Ding³

et al. 2017

Discrete Dynamics in Nature and Society

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Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

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“…To give a specific form for dynamics (10), in our model we also assume linear inverse demand function [5,9,10,13,14,18,23,24,26,[32][33][34]:…”

Section: Two Different Delay Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a Duopoly Game with Two Different Delay Structures

Jiang¹,

Xu²,

Ding³

et al. 2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…Puu [10,11] discussed the dynamical properties of the Cournot oligarchic model and 2 Discrete Dynamics in Nature and Society indicated that it will not converge to Nash equilibrium unless it is a complex trajectory. And the dynamical properties of the bounded rational duopoly model are also studied in [12].…”

Section: Introductionmentioning

confidence: 99%

Chaos Control and Anticontrol of the Output Duopoly Competing Evolution Model

Zhang

2017

Discrete Dynamics in Nature and Society

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In the process of social development, there are a lot of competitions and confrontations. Participants in these competitions and confrontations always have different interests and goals. In order to achieve their goals, the participants must consider the opponent's strategy to adjust their own strategies to achieve the interests of the optimization. This is called game. Based on the definition and its stability of the passive system, the passive control items are designed to the output of the duopoly competition evolution model, and the efficacy of the control methods is shown by the Lyapunov indexes. Then, the optimal function control method is taken to carry on the chaotic anticontrol to the chaotic system, and the Lyapunov indexes illustrate the control result. At last, the chaotic game of the system is introduced by combining the chaos control and anticontrol.

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“…In the dynamic study of economics, a couple of economic models represented by difference equations are investigated, such as the classical cobweb model describing the variation of the supply and demand, the Cournot models of oligopoly, and so on [2], [1], [6], [11]. It is well known that Bertrand duopoly competition game is one of the basic oligopoly games with two players.…”

Section: Introductionmentioning

confidence: 99%