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

Iraklis Kollias; Elias Camouzis; John Leventides

doi:10.3934/jdg.2017002

Article Contents

2017, Volume 4, Issue 1: 25-39. Doi: 10.3934/jdg.2017002

This issue Previous Article On repeated games with imperfect public monitoring: From discrete to continuous time Next Article Price of anarchy for graph coloring games with concave payoff

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
* Corresponding author

Received: June 30, 2016

Revised: October 31, 2016

Published: March 2018

Abstract Full Text(HTML) Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 91B02; Secondary: 91B24.

Citation:

Full Text(HTML)

Related Papers

Cited by

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.
[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.
[3]	E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations; With Open Problems and Conjectures Chapman & Hall/CRC Press, 2008.
[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.
[5]	A. Cournot, Recherches sur les Principes Mathematiques de la Theorie des Richesses Hachette, Paris, 1838.
[6]	A. Jakimowicz, Stability of the cournot-nash equilibrium in standard oligopoly, Acta Physica Polonica A, 121 (2012), 50-52.
[7]	T.-Y. Li and J. A. Yorke, Period three implies chaos, The American Mathematical Monthly, 82 (1975), 985-992.
[8]	T. E. Pallander, Konkurrens och marknadsj$ä$mvikt vid duopolo och oligopol, Ekonomisk Tidskrift, 41 (1939), 124-145,222--250.
[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.
[10]	R. D. Theocharis, On the stability of the cournot solution on the oligopoly problem, Review of Economic Studies, 27 (1959), 133-134.