The flip side of the Cournot - Nash competition

Abstract

The objective of this paper is to analyze the consequences of including en-
vironment 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 en-
vironment. 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.