Journal articles: 'Asymmetric dynamic duopoly model'

1

Caminal, Ramon. "A Dynamic Duopoly Model with Asymmetric Information." Journal of Industrial Economics 38, no. 3 (March 1990): 315. http://dx.doi.org/10.2307/2098501.

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Askar, S. S. "On Complex Dynamics of Differentiated Products: Cournot Duopoly Model under Average Profit Maximization." Discrete Dynamics in Nature and Society 2022 (March 9, 2022): 1–14. http://dx.doi.org/10.1155/2022/8677470.

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In this paper, some important dynamic characteristics such as multistability and synchronization phenomena are investigated for a game of an economic Cournot duopoly whose time evolution is received by the iteration of a noninvertible map in the plane. In the asymmetric case, the equilibrium points of game’s map are calculated, and their stability conditions are obtained. The obtained results show that the Nash equilibrium point loses its stability through flip bifurcation. Under some restrictions, the map’s coordinate axes form an invariant manifold, and hence their dynamics are studied based on a one-dimensional discrete dynamic map. In the symmetric case where both firms are identical, the map has the property of symmetry, and this implies that the diagonal q 1 = q 2 forms an invariant manifold and therefore synchronization phenomena occur. Global analysis of the behavior of the noninvertible map is carried out through studying critical manifolds of the map that categorize it as Z 4 − Z 2 − Z 0 type. Furthermore, global bifurcation of the basins of attraction is confirmed through contact between the critical curves and the boundaries of escaping domain.

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3

Yu, Weisheng, and Yu Yu. "The stability of Bayesian Nash equilibrium of dynamic Cournot duopoly model with asymmetric information." Communications in Nonlinear Science and Numerical Simulation 63 (October 2018): 101–16. http://dx.doi.org/10.1016/j.cnsns.2018.03.001.

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4

Sannikov, Yuliy, and Andrzej Skrzypacz. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production." American Economic Review 97, no. 5 (November 1, 2007): 1794–823. http://dx.doi.org/10.1257/aer.97.5.1794.

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We show that it is impossible to achieve collusion in a duopoly when (a) goods are homogenous and firms compete in quantities; (b) new, noisy information arrives continuously, without sudden events; and (c) firms are able to respond to new information quickly. The result holds even if we allow for asymmetric equilibria or monetary transfers. The intuition is that the flexibility to respond quickly to new information unravels any collusive scheme. Our result applies to both a simple stationary model and a more complicated one, with prices following a mean-reverting Markov process, as well as to models of dynamic cooperation in many other settings. (JEL D43, L12, L13)

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Jafari, Mostafa, Mohammad Mohammadpour omran, and Ehsan Jahani. "Offensive, Defensive, and Generic Advertising Strategies in a Dynamic Oligopolistic Market." Mathematical Problems in Engineering 2021 (April 7, 2021): 1–29. http://dx.doi.org/10.1155/2021/6633330.

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In today’s highly competitive business environment, advertisement plays an influential role in attracting customers and increasing market share. Companies adopt different advertising strategies in a competitive market, such as offensive, defensive, and generic, to keep and increase their market share. Researchers have generally modeled this problem using a dynamic differential game. All previous research studies have focused on finding these strategies in a duopoly market. Also, to simultaneously determine the optimal equilibrium strategy for these three strategies, the model is designed as a symmetric game due to the ease of solving. In contrast with the previous researches, the purpose of this paper is to present and solve an asymmetric game model to determine the optimal offensive, defensive, and generic advertising strategies in an oligopoly market. The proposed model’s objective is to obtain the maximum equilibrium profit for each company at any moment regarding the market share of each company and those of competitors. A numerical solution method based on the Pontryagin’s maximum principle is developed to solve the model. Then, the proposed model is solved for a triopoly market. Also, the sensitivity of the results to changes in model parameters has been investigated. The obtained results denote that in markets with more than two players under the asymmetric game, the proposed model can prescribe the optimal type of offensive, defensive, and generic advertising strategies.

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Askar, Sameh. "On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits." Symmetry 13, no. 12 (November 23, 2021): 2235. http://dx.doi.org/10.3390/sym13122235.

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This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

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7

Long, Jianjun, and Hui Huang. "Stability of equilibrium production-price in a dynamic duopoly Cournot-Bertrand game with asymmetric information and cluster spillovers." Mathematical Biosciences and Engineering 19, no. 12 (2022): 14056–73. http://dx.doi.org/10.3934/mbe.2022654.

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<abstract><p>Bounded rationality, asymmetric information and spillover effects are widespread in the economic market, and had been studied extensively in oligopoly games, however, few literature discussed the incomplete information between bounded rational oligopolists in an enterprise cluster. Considering the positive externalities brought by the spillover effect between cluster enterprises, a duopoly Cournot-Bertrand game with bounded rationality and asymmetric information is proposed in this paper. In our model, firm 1 with an information advantage knows all the price information of firm 2 with an information advantage, while firm 2 only partially knows the output information of firm 1, and they adopt boundedly rational expectation and naïve expectation respectively. Interestingly, our theoretical analysis reveals that: (1) When the output adjustment speed of enterprises with information advantage is large or the substitutability between monopoly products is high, moderate effective information is beneficial to the stability of product market, while too low or too high effective information may lead to market disorder. (2) The relationship between cluster spillover and Nash equilibrium stability depends on product substitutability. When the substitutability is small, smaller cluster spillovers are more conducive to the stability of product output or price; when the substitutability is large, the larger the cluster spillover is, the more stable the product market is. Our research has an important theoretical and practical significance to the production-price competition in oligopoly markets.</p></abstract>

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8

Joshi, Sumit. "Asymmetric outcome in a symmetric dynamic duopoly." Journal of Economic Dynamics and Control 31, no. 2 (February 2007): 531–55. http://dx.doi.org/10.1016/j.jedc.2005.12.001.

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9

Wang, Xia, Di Liu, and Jun-Pei Zhang. "Asymmetric Model of the Quantum Stackelberg Duopoly." Chinese Physics Letters 30, no. 12 (December 2013): 120302. http://dx.doi.org/10.1088/0256-307x/30/12/120302.

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10

Plummer, P. "Competitive Dynamics in Hierarchically Organized Markets: Spatial Duopoly and Demand Asymmetries." Environment and Planning A: Economy and Space 28, no. 11 (November 1996): 2021–40. http://dx.doi.org/10.1068/a282021.

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In recent years, there has been considerable interest in the impact of corporate organizational structure on the configuration of prices, outputs, and profits in spatially extensive markets. In previous research I examined the general and analytical conditions defining both the existence and stability of an equilibrium in hierarchically organized spatial markets dominated by oligopolistic corporations that distribute a commodity directly to consumers through their retail franchises. Here I examine the disequilibrium dynamics resulting from this model. A bilevel decisionmaking process is hypothesized in which corporations vary their delivered prices in response to changes in urban market demand and in which franchises vary their retail prices in response both to changes in the cost of the commodity from their parent corporation and to the pricing strategies pursued by their competitors. The complexity of interactions operating between the two levels of the model and the presence of asymmetrical demand conditions facing duopolistic corporations suggests that it is unlikely that an overall spatial price equilibrium can actually be reached by such disequilibrium price-adjustment strategies.

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11

Dockner, E. "Optimal pricing in a dynamic duopoly game model." Zeitschrift für Operations Research 29, no. 2 (April 1985): B1—B16. http://dx.doi.org/10.1007/bf01919488.

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12

Elsadany, A. A. "A dynamic Cournot duopoly model with different strategies." Journal of the Egyptian Mathematical Society 23, no. 1 (April 2015): 56–61. http://dx.doi.org/10.1016/j.joems.2014.01.006.

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13

Peng, Yu, Qian Lu, and Yue Xiao. "A dynamic Stackelberg duopoly model with different strategies." Chaos, Solitons & Fractals 85 (April 2016): 128–34. http://dx.doi.org/10.1016/j.chaos.2016.01.024.

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14

KIM, Jin-Ock. "Revisiting Dynamic Duopoly model: Implementing the Model using Software Python." Jeju National University Tourism, Business, and Economic Research Institute 40, no. 1 (February 28, 2020): 5–14. http://dx.doi.org/10.24907/jtir.2020.2.40.1.5.

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15

Wang, Xia, Jing Shen, and Zhengyao Sheng. "Asymmetric model of the quantum Stackelberg duopoly with incomplete information." Physics Letters A 384, no. 26 (September 2020): 126644. http://dx.doi.org/10.1016/j.physleta.2020.126644.

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16

Borkovsky, Ron N. "The timing of version releases: A dynamic duopoly model." Quantitative Marketing and Economics 15, no. 3 (August 19, 2017): 187–239. http://dx.doi.org/10.1007/s11129-017-9186-9.

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17

Ekhosuehi, Virtue U., and Augustine A. Osagiede. "On the dynamic duopoly model of non-price competition." Afrika Matematika 26, no. 5-6 (May 18, 2014): 923–38. http://dx.doi.org/10.1007/s13370-014-0257-8.

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18

Askar, S. S., and A. Al-khedhairi. "Cournot Duopoly Games: Models and Investigations." Mathematics 7, no. 11 (November 8, 2019): 1079. http://dx.doi.org/10.3390/math7111079.

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This paper analyzes Cournot duopoly games that are constructed based on Cobb–Douglas preferences. We introduce here two models whose dynamic adjustments depend on bounded rationality, dynamic adjustment, and tit-for-tat mechanism. In the first model, we have two firms with limited information and due to that they adopt the bounded rationality mechanism. They update their productions based on the changing occurred in the marginal profit. For this model, its fixed point is obtained and its stability condition is calculated. In addition, we provide conditions by which this fixed point loses its stability due to flip and Neimark–Sacker bifurcations. Furthermore, numerical simulation shows that this model possesses some chaotic behaviors which are recovered due to corridor stability. In the second model, we handle two different mechanisms of cooperation. These mechanisms are dynamic adjustment process and tit-for-tat strategy. The players who use the dynamic adjustment increase their productions based on the cooperative output while, in tit-for-tat mechanism, they increase the productions based on the cooperative profit. The local stability analysis shows that adopting tit-for-tat makes the model unstable and then the system becomes chaotic for any values of the system’s parameters. The obtained results show that the dynamic adjustment makes the system’s fixed point stable for a certain interval of the adjustment parameter.

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19

Bös, Dieter, and Lorenz Nett. "Privatization, price regulation, and market entry an asymmetric multistage Duopoly model." Journal of Economics 51, no. 3 (October 1990): 221–57. http://dx.doi.org/10.1007/bf01227423.

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20

Mendi, Pedro. "Backward integration and collusion in a duopoly model with asymmetric costs." Journal of Economics 96, no. 2 (July 31, 2008): 95–112. http://dx.doi.org/10.1007/s00712-008-0038-7.

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21

Pražák, Pavel, and Jaroslav Kovárník. "Nonlinear Phenomena in Cournot Duopoly Model." Systems 6, no. 3 (July 13, 2018): 30. http://dx.doi.org/10.3390/systems6030030.

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The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence.

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22

Escobido, M. G. O., and N. Hatano. "Critical slowing down in a dynamic duopoly." International Journal of Modern Physics: Conference Series 36 (January 2015): 1560012. http://dx.doi.org/10.1142/s2010194515600125.

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Anticipating critical transitions is very important in economic systems as it can mean survival or demise of firms under stressful competition. As such identifying indicators that can provide early warning to these transitions are very crucial. In other complex systems, critical slowing down has been shown to anticipate critical transitions. In this paper, we investigate the applicability of the concept in the heterogeneous quantity competition between two firms. We develop a dynamic model where the duopoly can adjust their production in a logistic process. We show that the resulting dynamics is formally equivalent to a competitive Lotka-Volterra system. We investigate the behavior of the dominant eigenvalues and identify conditions that critical slowing down can provide early warning to the critical transitions in the dynamic duopoly.

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23

Espinosa, M. Paz, and Petr Mariel. "A model of optimal advertising expenditures in a dynamic duopoly." Atlantic Economic Journal 29, no. 2 (June 2001): 135–61. http://dx.doi.org/10.1007/bf02299134.

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24

Chintagunta, Pradeep K., and Vithala R. Rao. "Pricing Strategies in a Dynamic Duopoly: A Differential Game Model." Management Science 42, no. 11 (November 1996): 1501–14. http://dx.doi.org/10.1287/mnsc.42.11.1501.

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25

Casadesus-Masanell, Ramon, and Pankaj Ghemawat. "Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows." Management Science 52, no. 7 (July 2006): 1072–84. http://dx.doi.org/10.1287/mnsc.1060.0548.

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26

Askar, Sameh S. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game." Mathematics 8, no. 7 (July 10, 2020): 1132. http://dx.doi.org/10.3390/math8071132.

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We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game’s equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles.

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27

Shi, Lian, Yun Le, and Zhaohan Sheng. "Analysis of Price Stackelberg Duopoly Game with Bounded Rationality." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/428568.

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The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.

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28

Long, Jianjun, and Hui Huang. "A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers." Discrete Dynamics in Nature and Society 2020 (October 16, 2020): 1–11. http://dx.doi.org/10.1155/2020/3251609.

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Many works studied on complex dynamics of Cournot or Stackelberg games, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase. Under the assumption that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Stackelberg–Cournot game with heterogeneous expectations is considered in this paper. Two firms with different R&D capabilities determine their R&D investments sequentially in the Stackelberg R&D phase and make output decisions simultaneously in the Cournot production phase. R&D spillovers, R&D investments, and technological innovation efficiency are introduced in our model. We find that: (i) the boundary equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is unstable if the Nash equilibrium of the system is strictly positive. (ii) The Nash equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is locally asymptotically stable only if the model parameters meet certain conditions. Especially, results indicate that small value of R&D spillovers or big value of output adjustment speed may yield bifurcations or even chaos. Numerical simulations are performed to exhibit maximum Lyapunov exponents, bifurcation diagrams, strange attractors, and sensitive dependence on initial conditions to verify our findings. It is also shown that the chaotic behaviors can be controlled with the state variables feedback and parameter variation method.

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29

Garmani, Hamid, Driss Ait Omar, Mohamed El Amrani, Mohamed Baslam, and Mostafa Jourhmane. "A Dynamic Duopoly Game with Content Providers’ Bounded Rationality." International Journal of Bifurcation and Chaos 30, no. 07 (June 15, 2020): 2050095. http://dx.doi.org/10.1142/s0218127420500959.

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This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.

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30

Zhou, Wei, Jie Zhou, Tong Chu, and Hui Li. "A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis." Complexity 2020 (August 11, 2020): 1–19. http://dx.doi.org/10.1155/2020/9634878.

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In this paper, a dynamic two-stage Cournot duopoly game with R&D efforts is built. Then, the local stability of the equilibrium points are discussed, and the stability condition of the Nash equilibrium point is also deduced through Jury criterion. The complex dynamical behaviors of the built model are investigated by numerical simulations. We found that the unique route to chaos is flip bifurcation, and the increase of adjusting speed will cause the system to lose stability and produce more complex dynamic behavior. In addition, we also found the phenomenon of multistability in the given model. Several kinds of coexistence of attractors are shown. In particular, we found that boundary attractors can coexist with internal attractors, which also aggravates the complexity of the system. At last, the chaotic state in the built system has been successfully controlled.

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31

de Goeij, Peter, and Wessel Marquering. "The generalized asymmetric dynamic covariance model." Finance Research Letters 2, no. 2 (June 2005): 67–74. http://dx.doi.org/10.1016/j.frl.2005.04.001.

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32

Chintagunta, Pradeep K., and Naufel J. Vilcassim. "Marketing investment decisions in a dynamic duopoly: A model and empirical analysis." International Journal of Research in Marketing 11, no. 3 (June 1994): 287–306. http://dx.doi.org/10.1016/0167-8116(94)90007-8.

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33

Yu, Weisheng, and Yu Yu. "A dynamic duopoly model with bounded rationality based on constant conjectural variation." Economic Modelling 37 (February 2014): 103–12. http://dx.doi.org/10.1016/j.econmod.2013.10.034.

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M. LEMEUNIER, SÉBASTIEN. "Determinants of quality incentives in a mutual fund duopoly." Bankers, Markets & Investors 163 (February 10, 2021): 14–23. http://dx.doi.org/10.54695/bmi.163.4647.

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While a trend of literature stresses that worse before-fee performing mutual funds set relatively high fees, we raise an issue about the determinants of quality incentives in a mutual fund market. With an economic model where mutual funds are vertically differentiated and in which all investors are sophisticated, we demonstrate that mutual funds with different quality levels adopt the same strategic fee-setting in any circumstances. This fee-setting strategy and the asymmetric information allow the opportunism of a low-quality mutual fund and induces the high-quality one to deliver a high level of quality.

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35

Hamidi, Maryam, Ferenc Szidarovszky, and Akio Matsumoto. "Some notes on dynamic oligopsonies." Pure Mathematics and Applications 30, no. 3 (October 1, 2022): 1–7. http://dx.doi.org/10.2478/puma-2022-0018.

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Abstract A special oligopoly model is considered when the firms compete on the factor market, and the used factor volumes determine their outputs. In the Nfirm case conditions are given for the existence of the Nash equilibrium, and in the cooperative case, sufficient conditions are derived for the existence and uniqueness of the joint profit maximizer. In the case of a linear duopoly the dynamic extensions are introduced in both cases based on gradient adjustments. Conditions are given for the local asymptotic stability of the equilibrium and the joint profit maximizer without and with information delays.

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36

Askar, Sameh S. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit." Mathematics 8, no. 10 (October 17, 2020): 1826. http://dx.doi.org/10.3390/math8101826.

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The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions.

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Angelini, Natascia, Roberto Dieci, and Franco Nardini. "Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules." Mathematics and Computers in Simulation 79, no. 10 (June 2009): 3179–96. http://dx.doi.org/10.1016/j.matcom.2009.04.001.

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Askar, S. S. "Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism." Mathematical Problems in Engineering 2020 (December 10, 2020): 1–12. http://dx.doi.org/10.1155/2020/6620570.

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We study a Bertrand duopoly game in which firms adopt a gradient-based mechanism to update their prices. In this competition, one of the firms knows somehow the price adopted by the other firm next time step. Such asymmetric information of the market price possessed by one firm gives interesting results about its stability in the market. Under such information, we use the bounded rationality mechanism to build the model describing the game at hand. We calculate the equilibrium points of the game and study their stabilities. Using different sets of parameter values, we show that the interior equilibrium point can be destabilized through flip and Neimark–Sacker bifurcations. We compare the region of stability of the proposed model with a classical Bertrand model without asymmetric information. The results show that the proposed game’s map is noninvertible with type Z 0 − Z 2 or Z 1 − Z 3 , while the classical model is of type Z 0 − Z 2 only. This explains the quite complicated basins of attraction given for the proposed map.

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TSENG, FAN-CHEN, and KUANG-CHENG ANDY WANG. "COMPATIBILITY STRATEGIES FOR AN ASYMMETRIC DUOPOLY CONSIDERING NETWORK EFFECTS AND MARKET SHARES." International Journal of Innovation and Technology Management 08, no. 04 (December 2011): 615–34. http://dx.doi.org/10.1142/s0219877011002581.

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The network effect is a key factor influencing the development of e-business and technological innovation. At the same time, compatibility decisions can determine the success or failure of businesses and technologies. This study explores the compatibility strategies in the context of network effects using a two-stage game-theoretical model for a duopoly. In the first stage, two firms make their compatibility decisions, and in the second stage, two firms are engaged in Bertrand price competition. Major findings are (1) other things being fixed, two firms are more likely to be compatible with each other when they have similar market shares, (2) the compatibility decisions of firms will not be influenced by consumers' switching costs, (3) the order of their compatibility decisions will not change the resulting equilibrium, and (4) based on firms' compatibility decisions, the Bertrand price competition may still lead to market failure, necessitating governmental intervention or regulations.

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40

Tan, Yingshuang, and Yong Long. "Option-Game Approach to Analyze Technology Innovation Investment under Fuzzy Environment." Journal of Applied Mathematics 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/830850.

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Based on the model of symmetric and asymmetric duopoly option game, this paper discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number. It constructs the fuzzy expressions of the investment value and investment threshold of followers and leaders under fuzzy environment and conducts numerical analysis. This offers a kind of explanation to the investment strategies under fuzzy environment.

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41

Fonseca, Miguel A. "Endogenous Price Leadership with Asymmetric Costs: Experimental Evidence." Studies in Microeconomics 7, no. 1 (June 2019): 59–74. http://dx.doi.org/10.1177/2321022219832736.

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This paper presents experimental evidence on the action commitment game with cost-asymmetric firms in a differentiated-products Bertrand duopoly. Unlike its quantity-setting counterpart, the risk-dominant leader–follower equilibrium Pareto dominates the simultaneous-move equilibrium. This equilibrium also minimizes payoff differences between firms. Hence, one would expect the model to accurately capture behavior. The evidence partially supports the theory: low-cost firms price in the first period more often than high-cost firms, and depending on the treatment, between 40 and 57 per cent of all observations conform to equilibrium play. However, the modal timing outcome involved both firms delaying their pricing decision. This timing outcome is characterized by Nash play and some collusion. The high frequency of delaying decisions could be due to a desire to reduce strategic uncertainty.

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42

Ginevičius, Romualdas, and Algirdas Krivka. "APPLICATION OF GAME THEORY FOR DUOPOLY MARKET ANALYSIS." Journal of Business Economics and Management 9, no. 3 (September 30, 2008): 207–17. http://dx.doi.org/10.3846/1611-1699.2008.9.207-217.

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The paper provides the analysis of game theory models application to identify duopoly market equilibrium (quantities sold and market prices), to evaluate and compare the results of enterprises in a market. The purpose of the analysis is to determine to what extent theoretical models correspond to real life, that is how reliable they are in supporting and estimating decisions of duopoly companies, fortifying market prices and quantities sold, evaluating company's competing positions and possibilities for decision co‐ordination. To describe discrete strategies equilibrium the “Prisoner's Dilemma” model is applied to a hypothetic market entrance game with possible side payments. Further analysis of the market entrance game incorporates mixed strategies based “Matching Pennies” model in case discrete strategies equilibrium does not exist. Continuous strategies are described analyzing hypothetic duopoly by applying Cournot, Stackelberg and Bertrand models. The first and the second mover advantage issues are raised comparing outcomes of dynamic Stackelberg and Bertrand games for a leader and a follower. Stability and utility of cartel agreement for its participants is mathematically supported with the help of a multi‐step repeated Cournot game. Having described, compared and applied the main game theory models to artificial duopoly market situations, the author passes over to the comparative analysis of the models’ weaknesses and problems related to their practical application.

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Bi, Wenjie, Yinghui Sun, Haiying Liu, and Xiaohong Chen. "Dynamic Nonlinear Pricing Model Based on Adaptive and Sophisticated Learning." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/791656.

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Existing dynamic pricing models which take consumers’ learning behavior into account generally assume that consumers learn on the basis of reinforcement learning and belief-based learning. Nevertheless, abundant empirical evidence of behavior game indicates that consumers’ learning is normally described as a process of mixed learning. Particularly, for experience goods, a consumer’s purchase decision is not only based on his previous purchase behavior (adaptive learning), but also affected by that of other consumers (sophisticated learning). With the assumption that consumers are both adaptive and sophisticated learners, we study a dynamic pricing model dealing with repeated decision problems in a duopoly market. Specifically, we build a dynamic game model based on sophisticated experience-weighted attraction learning model (SEWA) and analyze the existence of the equilibrium. Finally, we show the characteristics and differences of the steady-state solutions between models considering adaptive consumers and models considering sophistical consumers by numerical results.

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Li, Hao, Xi Yang, Yu Tu, and Ting Peng. "Two-Period Dynamic versus Fixed-Ratio Pricing Policies under Duopoly Competition." Mathematical Problems in Engineering 2019 (March 28, 2019): 1–11. http://dx.doi.org/10.1155/2019/6567952.

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This paper introduces a two-period, pricing policy under duopoly competition between two firms offering an identical product to consumers who are intertemporal utility maximization. Firms have equal inventories of faultlessly replaceable and perishable products. The firms adjust prices to maximize profits and determine optimal pricing policies, choosing from dynamic pricing, fixed-ratio pricing, and elastic pricing policies. According to a duopoly competition model, the consumer is limited to a single firm visit per period. The consumer decides to purchase the product at current price from a firm and remain in the market to purchase product from the other firm in the next period or exit the market. The results offer three main conclusions. First, elastic pricing is consistent with dynamic pricing. Second, the more consumers visit the firm in the first period, the more profits the firm will make. Third, we explore the effectiveness of different pricing policies. The results show that although dynamic pricing is a more complex policy than fixed-ratio pricing, it may lead to decreased equilibrium profits when the firms sharply discounts prices and consumer rationality is unlimited.

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Yu, Yu, and Weisheng Yu. "The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference." Applied Mathematics and Computation 395 (April 2021): 125852. http://dx.doi.org/10.1016/j.amc.2020.125852.

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Bi, Gongbing, Lechi Li, Feng Yang, and Liang Liang. "Dynamic Pricing Based on Strategic Consumers and Substitutes in a Duopoly Setting." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/694568.

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Based on the rational strategic consumers, we construct a dynamic game to build a two-period dynamic pricing model for two brands of substitutes which are sold by duopoly. The solution concept of the dynamic game is Nash equilibrium. In our model, consumers have been clearly segmented into several consumption classes, according to their expected value of the products. The two competing firms enter a pricing game and finally reach the state of Nash equilibrium. In addition, decision-making process with only myopic consumers existing in the market is analyzed. To make the paper more practical and realistic, the condition, in which the myopic and strategic consumers both exist in the market, is also considered and studied. In order to help the readers understand better and make it intuitively more clearly, a numerical example is given to describe the influence of the main parameters to the optimal prices. The result indicates that, to maintain the firms’ respective optimal profits, the prices of the products should be adjusted appropriately with the changes of product differentiation coefficient.

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Askar, S. S., Ahmad M. Alshamrani, and K. Alnowibet. "Analysis of Nonlinear Duopoly Game: A Cooperative Case." Discrete Dynamics in Nature and Society 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/528217.

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We make further attempts to investigate equilibrium stability of a nonlinear Cournot duopoly game. Our studies in this paper focus on the cooperation that may be obtained among duopolistic firms. Discrete time scales under the assumption of unknown inverse demand function and linear cost are used to build our models in the proposed games. We introduce and study here an adjustment dynamic strategy beside the so-called tit-for-tat strategy. For each model, the stability analysis of the fixed point is analyzed. Numerical simulations are carried out to show the complex behavior of the proposed models and to point out the impact of the models’ parameters on the cooperation.

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Wu, Fang, and Junhai Ma. "The Chaos Dynamic of Multiproduct Cournot Duopoly Game with Managerial Delegation." Discrete Dynamics in Nature and Society 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/206961.

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Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.

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Trifonov, Ju S., and B. S. Potanin. "Multivariate Asymmetric GARCH Model with Dynamic Correlation Matrix." Finance: Theory and Practice 26, no. 2 (April 29, 2022): 204–18. http://dx.doi.org/10.26794/2587-5671-2022-26-2-204-218.

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This study examines the problem of modeling the joint dynamics of conditional volatility of several financial assets under an asymmetric relationship between volatility and shocks in returns (leverage effect). We propose a new multivariate asymmetric conditional heteroskedasticity model with a dynamic conditional correlation matrix (DCC-EGARCH). The proposed method allows modelling the joint dynamics of several financial assets taking into account the leverage effect in the financial markets. DCC-EGARCH model has two main advantages over previously proposed multivariate asymmetric specifications. It involves a substantially simpler optimization problem and does away with the assumption of conditional correlation time invariance. These features make the model more suitable for practical applications. To study the properties of the obtained estimators, we conducted a simulated data analysis. As a result, we found statistical evidence in favor of the developed DCC-EGARCH model compared with the symmetric DCC-GARCH process in case of considering data with the presence of the leverage effect. Further, we applied the proposed method to analyze the joint volatility of Rosneft stock returns and Brent oil prices. By estimating the DCC-EGARCH model, we found statistical evidence for both the presence of the leverage effect in the oil price data and the presence of the dynamic correlation structure between the time series, which motivates the practical application of the proposed method.

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Cao, Yang, Ferrara Massimiliano, Gangemi Mariangela, and Guerrini Luca. "Hopf Bifurcation Analysis in a Modified R&D Model with Delay." Axioms 11, no. 4 (March 24, 2022): 148. http://dx.doi.org/10.3390/axioms11040148.

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We consider a duopoly game model of R&D (research and development) rivalry between two high-tech firms with time delay, in which a monopoly sector with R&D spillover is studied using a mixture of game theory and nonlinear dynamics theory. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the delay can lead the system dynamic behavior to exhibit stability switches and Hopf bifurcations appear.

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Journal articles on the topic 'Asymmetric dynamic duopoly model'

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