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With the prominence of global warming, national governments concentrate on carbon emission problems more and more and environmental regulations of governments have become the significant content of social regulations. Governments' supervision of carbon emission in order to realize low carbon emission reduction has become urgent affairs to relieve environmental pressure. This paper established a Bayes dynamic game model of government environment supervision authority and carbon emission enterprises. This paper introduced the monitoring system as the method of mastering enterprises' real time carbon emission for the first time and considered the situation of enterprises' disclosing their carbon information to avoid the examination of government authorities. From model analysis, this paper drew the conclusion that the accuracy of monitoring system and whether the enterprise announce its carbon information have great impact on the strategy choice of both sides in the game. The research results of this paper have great practical significance on improving carbon emission regulation policy, restraining over-emission and secret emission problems of enterprises and enhancing carbon emission regulation efficiency.