The flip side of the Cournot - Nash competition

  • M.M. Khoshyaran Economics Traffic Clinic - ETC, 34 Avenue des Champs Elyses, 75008, Paris France
Keywords: Competition; strategy; environment; environmental vectors; environmental attractors; orbits; reaction functions; payoff functions; player-environment interaction


The objective of this paper is to analyze the consequences of including environment of players in the Cournot-Nash competition. A two-persons non-cooperative game is considered. The environment is expressed in
terms of  others". The function of the environment is to maintain its equilibrium. The equilibrium point of the environment is upgraded if the strategies of one or both players have a favorable impact on the environment. The equilibrium stays at its previous level otherwise. The equilibrium point of the environment is called an environmental attractor. The environmental attractor aects the strategies of the players which in turn dene the reaction functions and the pay-o functions. It is shown that in the presence of an environmental attractor, players can not reach a Nash point. In fact the reaction functions of the players act as orbits around the environmental attractor. Thus each player has a nite but compact number of strategies compatible with the environment available to them. As long as the equilibrium of the environment is maintained, any of the orbits will be acceptable choices for the players. An environmental model of a two-persons competition game is given, and the consequences are studied.


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[1] J.W. Friedman, Game Theory with Applications to Economics, Oxford UniversityPress, Inc., New York 1986
[2] R. Aumann, S. Hart, Hand book of Game Theory with Economic Applications, Handbooks in Economics, vol.3, no.11 (2002).
[3] A. Granas, J. Dugundji, Fixed point Theory, Springer Verlag, New York 2003.
[4] A.D. Dalmedico, J.L. Chabert, K. Chemla, Chaos et determinisme, Edition deSeuil, Paris 1992.
[5] D. Ruelle, Hasard et Chaos, Edition Odile Jacob, Paris 2000.
[6] G. Giraud, La theorie des jeux, Edition Champs Universite, Flammarion, Paris2000.
[7] H. Poincare, Memoire sur les coubes definies par une equation differentielle, Journal de Mathematique, t.8, Uvres. I., 1882, p. 72.
[8] S. Banach, Theorie des operations Lineaire, Polish Science Journal, vol. 2, 1978.
[9] A. Granas, J. Dugundji, Fixed Point Theory, Springer -Verlag, New York 2003.
[10] J.M. Danskin, The Theory of Max-Min, Economics of Operation Research V,Springer -Verlag, New York 1967.
How to Cite
Khoshyaran, M. (2018). The flip side of the Cournot - Nash competition. Journal of Progressive Research in Mathematics, 13(1), 2118-2134. Retrieved from