The authors consider the problem of multi-player evolutionary game with two strategies and an arbitrary number of players. A randomised probabilistic access model is considered where the users randomly select the strategies. The strategies are a selection between two radio access technologies to receive service from. For a fair resource allocation between a number of users, the payoff function of each player is considered to be inversely proportional to the number of players choosing a strategy. It is valid for the radio access technology selection problem where resources are divided fairly between the users. The necessary and sufficient conditions for the existence and uniqueness of a mixed Nash equilibrium point of the game is provided. In addition, it is proved that the mixed Nash equilibrium point of the game is globally asymptotically stable and also evolutionarily stable strategy.