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Authors: Mihaela Neamtu Nicoleta Sirghi , Doriana Ramescu

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Abstract: This paper studies the cooperation or competition relationship from the perspective of dynamic games, where two and three firms are considered, respectively. The associated mathematical models are described by systems with nonlinear delayed differential equations. The equilibrium points are determined and the existence of the Hopf bifurcation is investigated. The conclusions and future works are provided.

Keywords: equilibrium points, Hopf bifurcation, replicator dynamics, stability REFERENCES [1] J. Alboszta, M. Jacek, Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay, Journal of Theoretical Biology, 231(2), 2004, pp. 175-179. [2] N. Ben Khalifa, R. El-Azouzi, Y. Hayel, Random time delays in evolutionary game dynamics, Proceedings of IEEE Control and Decision Conference (CDC), Osaka, Japan, 2015, pp. 3840- 3845. [3] N. B. Khalifa, El A. Rachid, H. Yezekael, Delayed evolutionary game dynamics with nonuniform interactions in two communities, Proceedings of IEEE Control and Decision Conference (CDC), Los Angeles, California, Dec. 2014. [4] N. B. Khalifa, El A. Rachid, H. Yezekael, Hopf Bifurcations in Replicator Dynamics with Distributed Delays, preprint arXiv:1703.06721, 2017. [5] R. Iijima, On delayed discrete evolutionary dynamics, Journal of Theoretical Biology, 300, 2012, pp. 1-6. [6] L. Ma, Y. Wang, The Tripartite Evolutionary Game Analysis of Collusive Behavior Regulation in EPR System, International Journal of Humanities and Management Sciences, 4(4), 2016. [7] M. Neamtu, Deterministic and stochastic Cournot duopoly games with tax evasion, WSEAS Transactions on Mathematics,

Cite this paper

Mihaela Neamtu Nicoleta Sirghi, Doriana Ramescu. (2017) Analysis of Cooperation and Competition Relationship among Two and Three Firms. International Journal of Economics and Management Systems, 2 , 336-341

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