# American Institute of Mathematical Sciences

January  2017, 4(1): 25-39. doi: 10.3934/jdg.2017002

## Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs

 National and Kapodistrian University of Athens, Department of Economics, Sofokleous 1, 10559, Athens, Greece

* Corresponding author

Received  July 2016 Revised  November 2016 Published  December 2016

In this article, we study the Cournot-Theocharis duopoly with variable marginal cost. We present sufficient conditions such that, both firms enter the market at any stage, remain in the market, and maximize their profit at any stage. We suggest cost implementation strategies, under which the market might benefit from the variability of marginal cost. We exhibit strategies, for which, the variability of marginal cost might be hazardous for the duopoly competitors. We prove that there exist cases, in which the market forms cycles of length six. Within each cycle, there is an interchange between monopolies and duopolies. Finally, we present some new ideas to establish monopoly convergence under certain monopoly conditions.

Citation: Iraklis Kollias, Elias Camouzis, John Leventides. Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs. Journal of Dynamics & Games, 2017, 4 (1) : 25-39. doi: 10.3934/jdg.2017002
##### References:
 [1] A. Agliari, L. Gardini and T. Puu, The dynamics of a triopoly Cournot game, Chaos, Solitons and Fractals, 11 (2000), 2531-2560.  doi: 10.1016/S0960-0779(99)00160-5.  Google Scholar [2] C. Burr, L. Gardini and F. Szidarovszky, Discrete time dynamic oligopolies with adjustment constraints, Journal of Dynamics and Games, 2 (2015), 65-87.  doi: 10.3934/jdg.2015.2.65.  Google Scholar [3] E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations; With Open Problems and Conjectures Chapman & Hall/CRC Press, 2008.  Google Scholar [4] J. S. Canovas, Reducing competirors in a Cournot-Theocharis oligopoly model, Journal of Difference Equations and Applications, 15 (2009), 153-165.  doi: 10.1080/10236190802006415.  Google Scholar [5] A. Cournot, Recherches sur les Principes Mathematiques de la Theorie des Richesses Hachette, Paris, 1838. Google Scholar [6] A. Jakimowicz, Stability of the cournot-nash equilibrium in standard oligopoly, Acta Physica Polonica A, 121 (2012), 50-52.   Google Scholar [7] T.-Y. Li and J. A. Yorke, Period three implies chaos, The American Mathematical Monthly, 82 (1975), 985-992.   Google Scholar [8] T. E. Pallander, Konkurrens och marknadsj$ä$mvikt vid duopolo och oligopol, Ekonomisk Tidskrift, 41 (1939), 124-145,222--250.   Google Scholar [9] T. Puu, Rational expectations and the Cournot-Theocharis problem Discrete Dynamics in Nature and Society (2006), Art. ID 32103, 11 pp. doi: 10.1155/DDNS/2006/32103.  Google Scholar [10] R. D. Theocharis, On the stability of the cournot solution on the oligopoly problem, Review of Economic Studies, 27 (1959), 133-134.   Google Scholar

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##### References:
 [1] A. Agliari, L. Gardini and T. Puu, The dynamics of a triopoly Cournot game, Chaos, Solitons and Fractals, 11 (2000), 2531-2560.  doi: 10.1016/S0960-0779(99)00160-5.  Google Scholar [2] C. Burr, L. Gardini and F. Szidarovszky, Discrete time dynamic oligopolies with adjustment constraints, Journal of Dynamics and Games, 2 (2015), 65-87.  doi: 10.3934/jdg.2015.2.65.  Google Scholar [3] E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations; With Open Problems and Conjectures Chapman & Hall/CRC Press, 2008.  Google Scholar [4] J. S. Canovas, Reducing competirors in a Cournot-Theocharis oligopoly model, Journal of Difference Equations and Applications, 15 (2009), 153-165.  doi: 10.1080/10236190802006415.  Google Scholar [5] A. Cournot, Recherches sur les Principes Mathematiques de la Theorie des Richesses Hachette, Paris, 1838. Google Scholar [6] A. Jakimowicz, Stability of the cournot-nash equilibrium in standard oligopoly, Acta Physica Polonica A, 121 (2012), 50-52.   Google Scholar [7] T.-Y. Li and J. A. Yorke, Period three implies chaos, The American Mathematical Monthly, 82 (1975), 985-992.   Google Scholar [8] T. E. Pallander, Konkurrens och marknadsj$ä$mvikt vid duopolo och oligopol, Ekonomisk Tidskrift, 41 (1939), 124-145,222--250.   Google Scholar [9] T. Puu, Rational expectations and the Cournot-Theocharis problem Discrete Dynamics in Nature and Society (2006), Art. ID 32103, 11 pp. doi: 10.1155/DDNS/2006/32103.  Google Scholar [10] R. D. Theocharis, On the stability of the cournot solution on the oligopoly problem, Review of Economic Studies, 27 (1959), 133-134.   Google Scholar
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