# The flip side of the Cournot - Nash competition

### Abstract

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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### References

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*Journal of Progressive Research in Mathematics*,

*13*(1), 2118-2134. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/1371

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