Dynamical analysis of a delayed monopoly game with a log-concave demand function

Elsadany, A. A.; Awad, A. L.

doi:10.1016/j.orl.2015.11.001

Cited by 25 publications

(15 citation statements)

References 9 publications

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“…in which we used, both at the numerator and at the denominator, the steady state identityq ε 1 (γ) =q ε 2 (γ) + γ π ′ 0 (q ε 2 (γ)) + h 1 (ε) coming from the first equation of (6). Using (18) in (15), after some algebraic manipulations we obtain…”

Section: Appendixmentioning

confidence: 99%

“…In both works a discrete time adjustment mechanism is considered. Subsequent contributions extended the investigations in several directions, taking into account different demand and cost functions [12,13,14,15], studying the effect of varying the price elasticity of demand [16], considering modelling approaches based on continuous differential equations [17,18] or on hybrid discrete-continuous equations [19]. For a survey about monopoly modelling, we refer to [20] However, an issue, already raised in [2,1], has never been studied.…”

Section: Introductionmentioning

confidence: 99%

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Monopoly models with time-varying demand function

Cavalli

Naimzada

2018

Communications in Nonlinear Science and Numerical Simulation

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We study a family of monopoly models for markets characterized by timevarying demand functions, in which a boundedly rational agent chooses output levels on the basis of a gradient adjustment mechanism. After presenting the model for a generic framework, we analytically study the case of cyclically alternating demand functions. We show that both the perturbation size and the agent's reactivity to profitability variation signals can have counterintuitive roles on the resulting period-2 cycles and on their stability. In particular, increasing the perturbation size can have both a destabilizing and a stabilizing effect on the resulting dynamics. Moreover, in contrast with the case of timeconstant demand functions, the agent's reactivity is not just destabilizing, but can improve stability, too. This means that a less cautious behavior can provide better performance, both with respect to stability and to achieved profits. We show that, even if the decision mechanism is very simple and is not able to always provide the optimal production decisions, achieved profits are very close to those optimal. Finally, we show that in agreement with the existing empirical literature, the price series obtained simulating the proposed model exhibit a significant deviation from normality and large volatility, in particular when underlying deterministic dynamics become unstable and complex.

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Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monopoly models with time-varying demand function

Cavalli

Naimzada

2018

Communications in Nonlinear Science and Numerical Simulation

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“…Considering that players are heterogeneous, some scholars studied the influence of players' different adjustment mechanisms on the dynamics of game model (see [33][34][35][36][37]). Some papers extended the decision mechanisms by considering that firms may refer to more than one period when they make decisions, and then delay decision was utilized (see [38][39][40][41]). The impacts of players' exact estimation on the evolutions of the dynamic system were considered in [42,43].…”

Section: Related Literaturementioning

confidence: 99%

“…We notice that firms may estimate the marginal profit by a weighted mean value of past few prices rather than instant price to smooth possible deviations (also cited as delay decision; see [38][39][40][41]). We include this mechanism here and consider one-period delay decision for simplification:…”

Section: Modelmentioning

confidence: 99%

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Guo

2017

Complexity

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This paper studies internal reference price effects when competitive firms face reference price effects and make decisions based on partial information, where their decision-making mechanism is modeled by a dynamic adjustment process. It is shown that the evolution of this dynamic adjustment goes to stabilization if both adjustment speeds are small and the complexity of this evolution increases in adjustment speeds. It is proved that the necessary condition for flip bifurcation or Neimark-Sacker bifurcation will occur with the increase of adjustment speed in two special cases. What is more, numerical simulations show that these bifurcations do occur. Then, the impacts of parameters on stability and profits are investigated and some management insights for firms with limited information to take advantage of reference price effects are provided.

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“…In particular, FODEs are preferred more than corresponding conventional integer-order models in such systems with crucial memory effects, such as economic, biological, and social models (Ahmed and Elgazzar, 2007). Recently, chaotic behaviors are reported to exist in outputs of some FODEs (Abdelaziz et al, 2018; Aghababa, 2014a; Elsadany and Matouk, 2015, Elsadany and Awad, 2016; Ghaziani et al, 2016; Huang et al, 2017; Li and Peng, 2004; Li et al, 2017a, 2017b; Matouk and Elsadany, 2014, 2016; Matouk et al, 2015; Tavazoei and Haeri, 2008).…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of fractional-order differentiated Cournot triopoly game

Al-khedhairi

2020

Journal of Vibration and Control

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The objective of the article is to study the dynamics of the proposed fractional-order Cournot triopoly game. Sufficient conditions for the existence and uniqueness of the triopoly game solution are obtained. Stability analysis of equilibrium points of the fractional-order game is also discussed. The conditions for the presence of Nash equilibrium point along with its global stability analysis are studied. The interesting dynamical behaviors of the arbitrary-order Cournot triopoly game are discussed. Moreover, the effects of seasonal periodic forcing on the game’s behaviors are examined. The 0–1 test is used to distinguish between regular and irregular dynamics of system behaviors. Numerical analysis is used to verify the theoretical results that are obtained, and revealed that the nonautonomous fractional-order model induces more complicated dynamics in the Cournot triopoly game behavior and the seasonally forced game exhibits more complex dynamics than the unforced one.

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Dynamical analysis of a delayed monopoly game with a log-concave demand function

Cited by 25 publications

References 9 publications

Monopoly models with time-varying demand function

Monopoly models with time-varying demand function

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Dynamical analysis of fractional-order differentiated Cournot triopoly game

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