Complex dynamics with three oligopolists

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.

show abstract

“…The case when = 1 has been studied by Puu [22]. In addition, the duopoly game has been studied by Agliari et al [60].…”

Section: Market Utilitymentioning

confidence: 99%

“…In such studies, the main concern is to study the complex dynamic characteristics of the game. For example, some complex dynamics of duopoly game were studied in [8,[21][22][23][24][25]. In practice, such game is close to the economic reality and it is widely deployed in oligopoly.…”

Section: Introductionmentioning

confidence: 99%

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

2018

View full text Add to dashboard Cite

show abstract

“…In this particular case, the decision of each firm only depends on the competitors' realized quantities of the previous period. This is the case which has been considered by Puu [20,21].…”

Section: The Modelmentioning

confidence: 99%

Multistability in a dynamic Cournot game with three oligopolists

Agiza

Bischi

Kopel

1999

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

The time evolution of a dynamic oligopoly game with three competing firms is modeled by a discrete dynamical system obtained by the iteration of a three-dimensional non-invertible map. For the symmetric case of identical players a complete analytical study of the stability conditions for the fixed points, which are Nash equilibria of the game, is given. For the situation of several coexisting stable Nash equilibria a numerical study of their basins of attraction is provided. This gives, evidence of the occurrence of global bifurcations at which the basins are transformed from simply connected sets into nonconnected sets, a basin structure which is peculiar of non-invertible maps. The presence of several coexisting attractors (or multistability) is observed even when complex attractors exist. Two different routes to complexity are presented: one related to the creation of more and more complex attractors; the other related to the creation of more and more complex structures of the basins. Starting from the benchmark case of identical players, the effects of heterogeneous behavior of the players, causing the loss of the symmetry properties of the dynamical system, are investigated through numerical explorations. # 1999 IMACS/ Elsevier Science B.V. All rights reserved.

show abstract

“…In a classic Cournot model, each firm is assumed to have naïve expectation and thus guesses that the opponent's output remains at the same level as in the previous period and then chooses a optimal production strategy in the current period. The classic research has paid much attention to the stability and the complex phenomena in the dynamics of a Cournot game played by players with naïve expectation (e.g., [2][3][4][5][6][7][8]). …”

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

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.

show abstract

Complex dynamics with three oligopolists

Cited by 104 publications

References 3 publications

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Multistability in a dynamic Cournot game with three oligopolists

Dynamics of a Duopoly Game with Two Different Delay Structures

Contact Info

Product

Resources

About