Protecting environment and developing economy are often conflicting and mutually restrictive. Based on balancing the conflict and the coordination between the two and from the perspective of integration of environmental responsibility and economic responsibility， and by considering the asymmetric information relationship between the auditing authorities and the heads of governmental agencies， this paper builds a multi-dimensional game model for analyzing the above issues. Multidimensional game takes into account the interaction of strategies between the two dimensions and other factors， revealing more profound and rich truth about such problems. Some proposals are put forward， such as auditing organs should pay attention to reviewing the performance of the heads of government agencies； reducing the identification cost of audit institutions and improving the ability of audit supervision； increasing the punishment of the heads of government agencies who perform their duties improperly， reducing the possibility of violations ；improving the coordination ability of the heads of government agencies to fulfill the two responsibilities and reducing the cost of fulfilling their responsibilities； improving the expected benefits of the heads of government institutions who perform their duties dutifully"， which are helpful to promote the implementation of fused audit and promote the coordinated development of environment and economy.