Environment Crisis Theorems1

Abstract: To study the interaction between the player's actions and environment in economic management game such as launching some projects with pollution in a certain area, we consider the relation between the player’s interests and the environment. We introduce a so-called gross interest- environment game and the concept of common hazard degree based on binary number and n-person non-cooperative game theory. It is studied that properties of players ’ utility functions and common hazard degree. Basic on the concept of N-M stable set in set of Nash equilibria, we prove environment crisis theorems. Our main results are as follows: if it is an Nash equilibrium that every enterprise launching the project with pollution and it is not an Nash equilibrium that every not doing, then it is the most probable to realize Nash equilibrium with the greatest common hazard degree. Key words: gross interest-environment game; common hazard degree; N-M stable set; environment crisis theore