Abstract
In this paper, the expressions of Coasian Theorem and the concept of public domain are discussed at the beginning. Based on it, this paper derived a mathematic logic about Coasian Theorem. At last, it proves that if the number of owners who protect the public property is more than one, and then rent dissipation will occur. In addition, the enthusiasm for property rights protector in the information symmetry is greater than in the case of asymmetric information. Therefore, in order to protect the property rights more effective, we need to give the property rights to only man, so that asymmetric information structure can be transformed into the symmetric information structure. At this point, the public domain has become the private domain, so rent dissipation disappears.