Dynamics of a bounded rational Cournot duopoly model with cooperation
Keywords:
Cournot's duopoly model, Cooperation in duopoly, Existence and Stability of Equilibrium, Simulation modeling.
Abstract
In this paper, a description of a Cournot duopoly model based on a general inverse demand function and a quadratic cost function is investigated. Existence and stability of equilibrium points are investigated analytically and numerically. Cooperation in duopoly is considered with “tit-for tat” strategy.
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References
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[27] Z. Wang, A. Szolnoki, M. Perc, “Rewarding evolutionary fitness with links between Populations promotes Cooperation,” J. Theor. Biol., 349(2014)50–56.
[28] K. Huang, T. Wang, Y. Cheng, X. Zheng, “Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game,” PLOS ONE , 10(3)(2015)1–10.
[29] K. Huang, Y. Cheng, X. Zheng, Y. Yang, “ Cooperative behavior evolution of small groups on interconnected networks,” Chaos Solitons Fractals, 80(…)90–95.
[30] S. Boccaletti, G. Bianconi, R. Criado, C.I. Del Genio, J. Gomez-Gardenes, M. Romance, I. Sendina-Nadal, Z. Wang, M. Zanin, “The structure and dynamics of multilayer networks, ” Phys. Rep., 544(2014)1–122.
[31] E. Ahmed, A.S. Hegazi, M.F. Elettreby, S.S. Askar, “On multi-team games. Physica A. 369(2006)809–816.
[32] M.F. Elettreby, Y. Cheng, “Dynamical analysis of a Cournot duopoly model, ” Journal of the Egyptian, 24(4)(2016)681-686.
[33] F. Szidarovszky, S. Yakowitz, “A new proof of the existence and uniqueness of the Cournot equilibrium,” Inter. Economic review, 18(3)(1977)787-789.
[34] V. Cafagna, P. Coccorese, “ Dynamical systems and the arising of cooperation in a Cournot duopoly,” Chaos, Solitons and Fractals, 25(3)(2005)655-664.
[35] S.S. Askar, A. M. Alshamrani, K. Alnowibet, “Analysis of nonlinear duoply game: A cooperative Case,” Discrete Dynamics in Nature and Society. Article ID 528217, 2015, 5 pages.
[2] S. S. Askar, “On complex dynamics of monopoly market,” Econ. Model, 31(2013)586–589.
[3] S. S. Askar, “The rise of complex phenomena in Cournot duopoly games due to demand functions without inflection points,” Commun. In Nonlinear Sci. and Numer. Simul., 19(2014) 1918–1925.
[4] S. S. Askar, “On Cournot-Bertrand competition with differentiated products,” Ann. Oper. Res. 223(2014)81-93.
[5] S. S. Askar, “The impact of cost uncertainty on Cournot duopoly game with concave demand function,” J. Appl.Math. and Comp., 232(2013)144-149.
[6] S. S. Askar, “Complex dynamic properties of Cournot duopoly games with convex and log-concave demand function,” Oper. Res. Lett., 42(2014)85–90.
[7] S. S. Askar, “The dynamic of economic games based on product differentiation,” J. Comput. Appl. Math., 268(2014)135–144.
[8] S. S. Askar, “The impact of cost uncertainty on Cournot oligopoly game with concave demand function,” Appl. Math. Comput. 232(2014)144–149.
[9] E. Ahmed, M.F. Elettreby, A.S. Hegazi, “On quantum team games. Int. J. Theor. Phys. 45(2006)907-913.
[10] S. S. Askar, “On dynamical multi-team Cournot game in exploitation of a renewable resource,” Chaos Solitons Fractals vol., 32(2014)264–268.
[11] A. K. Naimzada, L. Sbragia, “Oligopoly games with nonlinear Chaos demand and cost functions: two bounded rational adjustment processes,” Solitons Fractals vol., 29(2006). 707–722.
[12] T. Puu, “The chaotic monopolist,” Chaos Solitons Fractals, 5(1995)35–44.
[13] H. N. Agiza, A. S. Hegazi, A. A. Elsadany, “ The dynamics of Bowley’s model with bounded rationality. Chaos Solitons Fractals, 12(2001)1705–1717 .
[14] H. N. Agiza, A. A. Elsadany, “Nonlinear dynamics in the Cournot duopoly game with heterogeneous Players,” Physica A, 320(2003)512–524.
[15] T. Dubiel-Teleszynski, “Nonlinear dynamics in a heterogeneous in Nonlinear Sci. and Numer. Simul., 16(2011)296–308.
[16] H. N. Agiza, A. A. Elsadany, “Chaotic dynamics in nonlinear duopoly game with heterogeneous players,” Appl. Math. Comput., 149(2004)843–860.
[17] J. Zhang, Q. Da, Y. Wang, “Analysis of nonlinear duopoly game with heterogeneous players, ” Econ. Model., 24(2007)138–148.
[18] H. N. Agiza, A. A. Elsadany, M.M. El-Dessoky, “On a new Cournot duopoly game,” Journal of Chaos. Article ID 487803, 2013, 5 pages.
[19] Z. Ding, G. Shi, “Cooperation in a dynamical adjustment of duopoly game with incomplete information,” Chaos Solitons Fractals, 42(2009)989–993.
[20] C. Jung-Kyoo, “Trembles may support cooperation in a repeated prisoner’s dilemma game, ” J. Econ. Behav. Organ., 63(2007)384–393.
[21] R. Axelrod, The Evolution of Cooperation. Basic Books, New York, 1984.
[22] S. Kokubo, Z. Wang, J. Tanimoto, “Spatial reciprocity for discrete, continuous and mixed strategy setups,” Appl. Math. Comput., 259(2015)552–585.
[23] Z. Wang, L. Wang, A. Szolnoki, M. Perc, “Evolutionary games on multilayer networks: a colloquium,” Eur. Phys. J., 88(2015)124–138.
[24] X. Deng, Q. Liu, R. Sadiq, Y. Deng, “Impact of roles assignation on heterogeneous Populations in evolutionary dictator game,” Scientific reports, 4(2014), Article number 6937.
[25] Z. Wang, S. Kokubo, M. Jusup, J. Tanimoto, “ Universal scaling for the dilemma strength in evolutionary Games,” Phys. of Life Rev., 14(2015)1–30.
[26] Z. Wang, L. Wang, M. Perc, “Degree mixing in multilayer networks impedes the evolution of cooperation,” Phys. Rev. E., 89 (5)(2014), 052813.
[27] Z. Wang, A. Szolnoki, M. Perc, “Rewarding evolutionary fitness with links between Populations promotes Cooperation,” J. Theor. Biol., 349(2014)50–56.
[28] K. Huang, T. Wang, Y. Cheng, X. Zheng, “Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game,” PLOS ONE , 10(3)(2015)1–10.
[29] K. Huang, Y. Cheng, X. Zheng, Y. Yang, “ Cooperative behavior evolution of small groups on interconnected networks,” Chaos Solitons Fractals, 80(…)90–95.
[30] S. Boccaletti, G. Bianconi, R. Criado, C.I. Del Genio, J. Gomez-Gardenes, M. Romance, I. Sendina-Nadal, Z. Wang, M. Zanin, “The structure and dynamics of multilayer networks, ” Phys. Rep., 544(2014)1–122.
[31] E. Ahmed, A.S. Hegazi, M.F. Elettreby, S.S. Askar, “On multi-team games. Physica A. 369(2006)809–816.
[32] M.F. Elettreby, Y. Cheng, “Dynamical analysis of a Cournot duopoly model, ” Journal of the Egyptian, 24(4)(2016)681-686.
[33] F. Szidarovszky, S. Yakowitz, “A new proof of the existence and uniqueness of the Cournot equilibrium,” Inter. Economic review, 18(3)(1977)787-789.
[34] V. Cafagna, P. Coccorese, “ Dynamical systems and the arising of cooperation in a Cournot duopoly,” Chaos, Solitons and Fractals, 25(3)(2005)655-664.
[35] S.S. Askar, A. M. Alshamrani, K. Alnowibet, “Analysis of nonlinear duoply game: A cooperative Case,” Discrete Dynamics in Nature and Society. Article ID 528217, 2015, 5 pages.
Published
2019-07-16
How to Cite
Foul, A. (2019). Dynamics of a bounded rational Cournot duopoly model with cooperation. Journal of Progressive Research in Mathematics, 15(2), 2609-2623. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1742
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