Journal articles: 'Duopoly games'

1

Li, Risong, Hongqing Wang, and Yu Zhao. "Kato’s chaos in duopoly games." Chaos, Solitons & Fractals 84 (March 2016): 69–72. http://dx.doi.org/10.1016/j.chaos.2016.01.006.

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2

Dana, Rose-Anne, and Luigi Montrucchio. "Dynamic complexity in duopoly games." Journal of Economic Theory 40, no. 1 (October 1986): 40–56. http://dx.doi.org/10.1016/0022-0531(86)90006-2.

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3

Li, Risong, Yu Zhao, Tianxiu Lu, Ru Jiang, Hongqing Wang, and Haihua Liang. "Spatio-temporal chaos in duopoly games." Journal of Nonlinear Sciences and Applications 10, no. 07 (July 23, 2017): 3784–91. http://dx.doi.org/10.22436/jnsa.010.07.33.

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4

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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5

Cánovas, José S., and Antonio Linero. "Topological dynamic classification of duopoly games." Chaos, Solitons & Fractals 12, no. 7 (June 2001): 1259–66. http://dx.doi.org/10.1016/s0960-0779(00)00098-9.

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6

MATSUMOTO, AKIO, and FERENC SZIDAROVSZKY. "NONLINEAR DUOPOLY GAMES WITH ADVERTISEMENT REVISITED." International Game Theory Review 12, no. 04 (December 2010): 363–84. http://dx.doi.org/10.1142/s0219198910002726.

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This study reconsiders a duopoly model with advertisement introduced earlier by Ahmed, Agiza and Hassan [1999]. It demonstrates three major findings. The first is that the model can be destabilized via either flip bifurcation or Hopf bifurcation. The second is that a half-pitchfork bifurcation of the output occurs when the advertisement dynamics is periodic and the nonlinearity of the output dynamics becomes stronger. Finally the third is that the existence of attractor and the coexistence of attracting sets are the main features of the model when it is locally unstable.

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7

von Stengel, Bernhard. "Follower payoffs in symmetric duopoly games." Games and Economic Behavior 69, no. 2 (July 2010): 512–16. http://dx.doi.org/10.1016/j.geb.2009.10.012.

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8

Stanford, William. "Prestable strategies in discounted duopoly games." Games and Economic Behavior 3, no. 1 (February 1991): 129–44. http://dx.doi.org/10.1016/0899-8256(91)90009-4.

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9

Lambertini, Luca. "Prisoners' Dilemma in Duopoly (Super)Games." Journal of Economic Theory 77, no. 1 (November 1997): 181–91. http://dx.doi.org/10.1006/jeth.1997.2328.

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10

Frąckiewicz, Piotr, and Jakub Bilski. "Quantum Games with Unawareness with Duopoly Problems in View." Entropy 21, no. 11 (November 10, 2019): 1097. http://dx.doi.org/10.3390/e21111097.

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Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model.

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Cánovas, J. S., and M. Ruı́z Marı́n. "Chaos on MPE-sets of duopoly games." Chaos, Solitons & Fractals 19, no. 1 (January 2004): 179–83. http://dx.doi.org/10.1016/s0960-0779(03)00156-5.

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12

Italo Bischi, Gian, Cristiana Mammana, and Laura Gardini. "Multistability and cyclic attractors in duopoly games." Chaos, Solitons & Fractals 11, no. 4 (March 2000): 543–64. http://dx.doi.org/10.1016/s0960-0779(98)00130-1.

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13

Matsumura, Toshihiro. "ENDOGENOUS TIMING IN MULTI-STAGE DUOPOLY GAMES." Japanese Economic Review 46, no. 3 (September 1995): 257–65. http://dx.doi.org/10.1111/j.1468-5876.1995.tb00016.x.

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14

Cánovas, J. S., and S. Paredes. "On the control of some duopoly games." Mathematical and Computer Modelling 52, no. 7-8 (October 2010): 1110–15. http://dx.doi.org/10.1016/j.mcm.2010.03.009.

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15

Ray, Indrajit, and Sonali Sen Gupta. "Coarse correlated equilibria in linear duopoly games." International Journal of Game Theory 42, no. 2 (December 6, 2012): 541–62. http://dx.doi.org/10.1007/s00182-012-0360-8.

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16

Lu, Tianxiu, and Peiyong Zhu. "Further discussion on chaos in duopoly games." Chaos, Solitons & Fractals 52 (July 2013): 45–48. http://dx.doi.org/10.1016/j.chaos.2013.03.012.

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17

Yang, Xiao Hua, and Sheng Li Chen. "A Note on Endogenous Timing in Duopoly Games." Advanced Materials Research 204-210 (February 2011): 545–49. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.545.

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We provide a general analysis of duopoly game in endogenous timing. The Nash equilibrium outcomes are compared with Stackelberg equilibrium outcomes. The different sets of conditions are provided for yielding respectively simultaneous and sequential plays and these conditions only depend on the monotonicities of the reaction functions and the payoffs functions in rival strategic variables.

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18

Zhao, Yu, and Risong Li. "Chaos in Duopoly Games via Furstenberg Family Couple." Complexity 2019 (November 23, 2019): 1–8. http://dx.doi.org/10.1155/2019/5484629.

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Assume that H1 and H2 are two given closed subintervals of ℝ and that f2:H1⟶H2 and f1:H2⟶H1 are continuous maps. Let ϒh1,h2=f1h2,f2h1 be a Cournot map over the space H1×H2. In this paper, we study G1,G2-chaos (resp. strong G1,G2-chaos) of such a Cournot map. We will show that the following are true: (1) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if Γ2Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (2) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1∪Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (3) f1∘f2 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if so is f2∘f1. MR(2000) Subject Classification: Primary 37D45, 54H20, and 37B40 and Secondary 26A18 and 28D20.

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19

Askar, S. S., Ahmad M. Alshamrani, and K. Alnowibet. "The arising of cooperation in Cournot duopoly games." Applied Mathematics and Computation 273 (January 2016): 535–42. http://dx.doi.org/10.1016/j.amc.2015.10.027.

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20

WENZELBURGER, JAN. "LEARNING TO PLAY BEST RESPONSE IN DUOPOLY GAMES." International Game Theory Review 06, no. 03 (September 2004): 443–59. http://dx.doi.org/10.1142/s0219198904000290.

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We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response behavior of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, a firm is able to play best response in the usual game theoretic sense.

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21

LAHMANDI-AYED, RIM. "DYNAMIC ENTRY GAMES: THE CASE OF NATURAL DUOPOLY." International Game Theory Review 08, no. 04 (December 2006): 701–13. http://dx.doi.org/10.1142/s021919890600120x.

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In the case of natural duopoly, we suggest a finitely repeated game between two incumbent firms and a potential entrant that limits the incumbent firms' power and compels them to approach economic efficiency. We prove that such a game admits a perfect subgame equilibrium along which the incumbent firms maintain with equal quantities while preventing entry. Moreover, the incumbents' strategies along this path converge to average cost pricing quantities as the number of periods goes to infinity.

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22

Askar, S. S., Ahmad M. Alshamrani, and K. Alnowibet. "Dynamic Cournot duopoly games with nonlinear demand function." Applied Mathematics and Computation 259 (May 2015): 427–37. http://dx.doi.org/10.1016/j.amc.2015.02.072.

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23

ALTMAN, EITAN, ODILE POURTALLIER, ALAIN HAURIE, and FRANCESCO MORESINO. "APPROXIMATING NASH EQUILIBRIA IN NONZERO-SUM GAMES." International Game Theory Review 02, no. 02n03 (June 2000): 155–72. http://dx.doi.org/10.1142/s0219198900000123.

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This paper deals with the approximation of Nash equilibria in m-player games. We present conditions under which an approximating sequence of games admits near-equilibria that approximate near-equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games, and (ii) a stochastic game played under the S-adapted information structure approximated by games played over a sampled event tree. Numerical illustrations show the usefulness of this approximation theory.

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24

Ohnishi, Kazuhiro. "PRICE-SETTING MIXED DUOPOLY, SUBSIDIZATION AND THE ORDER OF FIRMS’ MOVES: SUBSTITUTIVE, INDEPENDENT AND COMPLEMENTARY GOODS." INDIAN JOURNAL OF ECONOMICS AND FINANCIAL ISSUES 3, no. 1 (2022): 149–55. http://dx.doi.org/10.47509/ijefi.2022.v03i01.09.

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This paper uses a mixed Bertrand duopoly model comprising a public firm and a private firm, and investigates the role that production subsidies play in the mixed duopoly model regarding privatization and efficiency. The paper considers substitutive, independent and complementary goods, and examines the following three games: (i) the public firm and the private firm simultaneously and independently set their own prices, (ii) the public firm acts as a Stackelberg leader, and (iii) both firms act simultaneously and independently as profit-maximizers. The paper solves the three games and demonstrates that under the optimal subsidy of each of substitutive, independent and complementary goods, both firms’ profits, prices, outputs and economic welfare are respectively identical regardless of the nature of the competition.

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25

Goerg, Sebastian J., and Reinhard Selten. "Experimental investigation of stationary concepts in cyclic duopoly games." Experimental Economics 12, no. 3 (June 24, 2009): 253–71. http://dx.doi.org/10.1007/s10683-009-9218-8.

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26

G, Selin Savaşkan, and Aykut Or. "The Cournot Model of Duopoly and Interval Matrix Games." International Journal of Mathematics Trends and Technology 66, no. 4 (April 25, 2020): 211–16. http://dx.doi.org/10.14445/22315373/ijmtt-v66i4p524.

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27

Hamilton, Jonathan H., and Steven M. Slutsky. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria." Games and Economic Behavior 2, no. 1 (March 1990): 29–46. http://dx.doi.org/10.1016/0899-8256(90)90012-j.

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28

FURTH, DAVE. "DUOPOLY MODELS WITH VERTICAL PRODUCT DIFFERENTIATION." International Game Theory Review 13, no. 02 (June 2011): 121–40. http://dx.doi.org/10.1142/s0219198911002903.

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This paper deals with duopoly models with vertical product differentiation. These are two-stage games. In the first stage, the quality game, the two firms choose their quality. In the second stage, the price game, they choose their prices. When the market is covered, the properties of this game are well known, even when the consumers are not uniformly distributed. When the market is uncovered the literature is not always clear about these models. In the present paper it is shown that the price game can be solved, when the consumers are distributed according to a distribution function with a log-concave density function.

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29

Crespi, Giovanni Paolo, Davide Radi, and Matteo Rocca. "Robust games: theory and application to a Cournot duopoly model." Decisions in Economics and Finance 40, no. 1-2 (October 3, 2017): 177–98. http://dx.doi.org/10.1007/s10203-017-0199-3.

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30

Lee, M. Jin, M. Jae Moon, and Jungsook Kim. "Insights from experiments with duopoly games: rational incremental decision-making." Public Management Review 19, no. 9 (February 14, 2017): 1328–51. http://dx.doi.org/10.1080/14719037.2017.1282002.

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31

Feichtinger, G., and E. Dockner. "Optimal pricing in a duopoly: A noncooperative differential games solution." Journal of Optimization Theory and Applications 45, no. 2 (February 1985): 199–218. http://dx.doi.org/10.1007/bf00939977.

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32

Leppänen, Ilkka. "Evolutionarily stable conjectures and other regarding preferences in duopoly games." Journal of Evolutionary Economics 28, no. 2 (August 26, 2017): 347–64. http://dx.doi.org/10.1007/s00191-017-0529-1.

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33

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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34

Marini, Marco A., and Giorgio Rodano. "Lead, Follow or Cooperate? Sequential versus Collusive Payoffs in Symmetric Duopoly Games." ISRN Economics 2013 (November 6, 2013): 1–10. http://dx.doi.org/10.1155/2013/645481.

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In many strategic settings comparing the payoffs obtained by players under full cooperation to those obtainable at a sequential (Stackelberg) equilibrium can be crucial to determine the outcome of the game. This happens, for instance, in repeated games in which players can break cooperation by acting sequentially, as well as in merger games in which firms are allowed to sequence their actions. Despite the relevance of these and other applications, no full-fledged comparisons between collusive and sequential payoffs have been performed so far. In this paper we show that even in symmetric duopoly games the ranking of cooperative and sequential payoffs can be extremely variable, particularly when the usual linear demand assumption is relaxed. Not surprisingly, the degree of strategic complementarity and substitutability of players’ actions (and, hence, the slope of their best replies) appears decisive to determine the ranking of collusive and sequential payoffs. Some applications to endogenous timing are discussed.

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35

Al-khedhairi, Abdulrahman. "Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 3-4 (May 26, 2020): 339–59. http://dx.doi.org/10.1515/ijnsns-2019-0090.

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AbstractCournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order derivatives. Sufficient conditions for existence and uniqueness of the new model’s solution are obtained. The existence and local stability analysis of Nash equilibrium points along with other equilibrium points are examined. Some aspects of global stability analysis are treated. More significantly, the effects of seasonal periodic perturbations of parameters values are also explored. The multiscale fuzzy entropy measurements for complexity are employed for this case. Numerical simulations are presented in order to verify the analytical results. It is observed that the time-varying parameters induce very complicated dynamics in perturbed Cournot duopoly game compared with the unperturbed game.

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36

Wei, Longfei, Haiwei Wang, Jing Wang, and Jialong Hou. "Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market." Discrete Dynamics in Nature and Society 2021 (June 19, 2021): 1–18. http://dx.doi.org/10.1155/2021/3985367.

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This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

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37

Li, Changying, and Jianhu Zhang. "Dynamic Games of R&D Competition in a Differentiated Duopoly." Journal of Institutional and Theoretical Economics 169, no. 4 (2013): 660. http://dx.doi.org/10.1628/093245613x671184.

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38

Bischi, Gian-Italo, and Fabio Lamantia. "Nonlinear duopoly games with positive cost externalities due to spillover effects." Chaos, Solitons & Fractals 13, no. 4 (March 2002): 701–21. http://dx.doi.org/10.1016/s0960-0779(01)00006-6.

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39

Wang, Hongqing, Tianxiu Lu, Risong Li, Yuanlin Chen, Yongjiang Li, and Weizhen Quan. "Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games." Mathematics 10, no. 22 (November 12, 2022): 4226. http://dx.doi.org/10.3390/math10224226.

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By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction functions are studied. It is observed that a Cournot onto map H on a product space is sensitive (collectively sensitive, collectively accessible, accessible, or collectively Kato chaotic) if and only if the restriction of the map H2 to the MPE-set is sensitive as well. Several examples are given to show the necessity of the reaction functions being continuous onto maps.

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40

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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41

Sarafopoulos, Georges, and Kosmas Papadopoulos. "Chaos in Oligopoly Models." International Journal of Productivity Management and Assessment Technologies 7, no. 1 (January 2019): 50–76. http://dx.doi.org/10.4018/ijpmat.2019010104.

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In this article, the authors investigate the dynamics of two oligopoly games. In the first game, they consider a nonlinear Cournot-type duopoly game with homogeneous goods and same rational expectations. The authors investigate the case, where managers have a variety of attitudes toward relative performance that are indexed by their type. In the second game they consider a Cournot-Bertrand duopoly game with linear demand, quadratic cost function and differentiated goods. In the two games they suppose a linear demand and a quadratic cost function. The games are modeled with a system of two difference equations. Existence and stability of equilibria of the systems are studied. The authors show that the models gives more complex, chaotic and unpredictable trajectories, as a consequence of change in the parameter k of speed of the player's adjustment (in the first game) and in the parameter d of the horizontal product differentiation (in the second game). The authors prove that the variation of the parameter k (resp. d) destabilizes the Nash equilibrium via a period doubling bifurcation (resp. through a Neimark-Sacker bifurcation). The chaotic features are justified numerically via computing Lyapunov numbers and sensitive dependence on initial conditions. In the second game they show that in the case of a quadratic cost there are stable trajectories and a higher or lower degree of product differentiation does not tend to destabilize the economy. They verify these results through numerical simulations. Finally, the authors control the chaotic behavior of the games introducing a new parameter. For some values of this parameter, the Nash equilibrium is stable for every value of the main parameter k or d.

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42

Li, Jinlu. "Split Equilibrium Problems for Related Games and Applications to Economic Theory." International Game Theory Review 20, no. 04 (November 18, 2018): 1850005. http://dx.doi.org/10.1142/s0219198918500056.

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In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan–KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As an application of this existence to economics, an example is provided that studies the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual (playing twice) extended Bertrand duopoly model of price competition.

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43

Al-khedhairi, A. "Differentiated Cournot duopoly game with fractional-order and its discretization." Engineering Computations 36, no. 3 (April 8, 2019): 781–806. http://dx.doi.org/10.1108/ec-07-2018-0333.

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PurposeFractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims to explore a proposed fractional-order differentiated Cournot duopoly game and its discretized game.Design/methodology/approachConditions for existence and uniqueness of the proposed game’s solution are derived. The existence of Nash equilibrium point and its local and global stability are obtained. Furthermore, local stability analysis of the discretized game is investigated. The effects of fractional-order on game’s dynamics are examined, along with other parameters of the game, via the 2D bifurcation diagrams in planes of system’s parameters are acquired.FindingsTheoretical and numerical simulation results demonstrate rich variety of interesting dynamical behaviors such as period-doubling and Neimark–Sacker bifurcations, attractors’ crises in addition to chaotic attractors. The results demonstrated that the stability Nash equilibrium point of the game can be lost by period doubling or Neimark–Sacker bifurcations.Practical implicationsOligopoly games are pivotal in the mathematical modeling of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also macroeconomic analysis of business cycles, innovation and growth.Originality/valueAlthough the Cournot game and its variants have attracted great interest among mathematicians and economists since the time of its proposition till present, memory effects in continuous-time and discrete-time Cournot duopoly game have not been addressed yet. To the best of author’s knowledge, this can be considered as the first attempt to investigate this problem of fractional-order differentiated Cournot duopoly game. In addition, studying more realistic models of Cournot oligopoly games plays a pivotal role in the mathematical investigation and better understanding of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also in macroeconomic analysis of business cycles, innovation and growth.

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44

Askar, S. S., and A. Al-khedhairi. "Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control." Discrete Dynamics in Nature and Society 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/2585708.

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Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

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45

Beach, Robert. "Numerical Methods for Differential Games: Capital Structure in an R&D Duopoly." International Journal of Economics and Finance 9, no. 2 (January 11, 2017): 46. http://dx.doi.org/10.5539/ijef.v9n2p46.

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This paper compares two different numerical methods used to solve the same differential game. In differential games strategies of individual players are represented as continuous functions of time and are typically solutions to the optimal control problems of the players. The game is an R&D duopoly with two players: an upstream firm that is primarily engaged in research and development (the R&D firm) and whose value comes from the market valuation of these activities, and a downstream firm primarily engaged in distribution and marketing (the D&M firm). The first method is assumed to be the benchmark since it is based on discretizing the first order conditions of each player’s optimal control problem. The second method is based on making random guesses of the parameters of a second order polynomial and searching for optimal solutions. The results suggest that the second method, which is more automated and has the potential of being applied to games with higher dimensionality, can give approximate solutions to differential games similar to the one considered here. The results also provide an important theoretical outcome. They illustrate that unlike the tradeoff and pecking order models of capital structure there are many markets in which capital structure is not driven by a reversion to a target debt-to-equity ratio or a pecking order, but by maximizing firm value under strategic considerations.

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Geraskin, M. I. "Reflexive Games in the Linear Stackelberg Duopoly Models under Incoincident Reflexion Ranks." Automation and Remote Control 81, no. 2 (February 2020): 302–19. http://dx.doi.org/10.1134/s0005117920020095.

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Yanase, Akihiko. "Global environment and dynamic games of environmental policy in an international duopoly." Journal of Economics 97, no. 2 (March 26, 2009): 121–40. http://dx.doi.org/10.1007/s00712-009-0068-9.

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Matsumoto, Akio, and Ferenc Szidarovszky. "Stability, Bifurcation, and Chaos inN-Firm Nonlinear Cournot Games." Discrete Dynamics in Nature and Society 2011 (2011): 1–22. http://dx.doi.org/10.1155/2011/380530.

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AnN-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in whichNis divided into two groups and the other in whichNis divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly) and three-firm (triopoly) models to shed light on roles of the number of the firms.

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Castro, Luis E., and Nazrul I. Shaikh. "Optimal Advertisement Spending in a Duopoly with Incomplete Information." International Journal of Business Analytics 5, no. 3 (July 2018): 1–21. http://dx.doi.org/10.4018/ijban.2018070101.

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This article presents the relationship between a firm's advertisement spending and sales in a duopoly when information about the competitors' advertisement spending is unavailable. The competitive interaction between the firms has been modeled as imperfect information Cournot and Stackelberg games and the conditions for subgame perfect Bayesian Nash equilibrium are presented. The results suggest that when the firms are similar in size and advertisement effectiveness, both firms are better off sharing their advertising plans with each other. On the other hand, when one of the firms is a market leader, the follower may profit from the leader's advertisement spending and so is better off keeping the leader guessing. A practical approach to estimate the optimum advertisement budget based on the expected values of the competitors' historic advertising spending is presented as well.

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Askar, S. S., and A. Al-khedhairi. "Complexity Analysis of a 2D-Piecewise Smooth Duopoly Model: New Products versus Remanufactured Products." Complexity 2022 (April 30, 2022): 1–12. http://dx.doi.org/10.1155/2022/8856009.

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Recent studies on remanufacturing duopoly games have handled them as smooth maps and have observed that the bifurcation types that occurred in such maps belong to generic classes like period-doubling or Neimark-Sacker bifurcations. Since those games yield piecewise smooth maps, their bifurcations belong to the so-called border-collision bifurcations, which occur when the map’s fixed points cross the borderline between the smooth regions in the phase space. In the current paper, we present a proper systematic analysis of the local stability of the map’s fixed points both analytically and numerically. This includes studying the border-collision bifurcation depending on the map’s parameters. We present different multistability scenarios of the dynamics of the game’s map and show different types of periodic cycles and chaotic attractors that jump from one region to another or just cross the borderline in the phase space.

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Journal articles on the topic 'Duopoly games'

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