The increasing number of radiocommunication technologies and the Cross-border Interference (CBI) caused by ionospheric and tropospheric scatter, multipath reflection and diffraction are deteriorating the lack of spectrum re sources in border areas. Sharing spectrum seems to be the only way to reduce the chance of such harmful interference and increase the efficiency of the usage of spectrum. However, spectrum sharing in border areas can be tricky because incumbents and spectrum operators from different countries may have different goals for each frequency band. Take Canada and the US as an example, USA has employed CBRS with centralized control on 3500 MHz frequency band however, Canada is pursuing exclusive licensing. This paper is going to propose a new spectrum sharing mechanism that can be used in Canada-US border areas. We first study the existing cross-border frequency management solutions including the Harmonized Calculation Method (HCM) agreement, the Licensed Shared Access (LSA) dynamic spectrum sharing system and its advanced evolution Cross border LSA (CBLSA). We explore the advantage and disadvantage of the existing solutions. We then explore a recent research direction related to non-cooperative Game Theory and Nash Equilibrium to overcome the disadvantages. We go through several researches which use non-cooperative Game Theory to model the spectrum management issues between operators in different countries, and the primary users and secondary users in general. We list some of their results to show that this is indeed a possible way to solve the spectrum management issues in the border areas between Canada and the US. We finally conclude the non cooperative Game Theory approach with its Technology Readiness Level (TRL) to indicate its progress towards a final solution to the problem and the future work that needs to be done.