Cognitive radio enabled wireless sensor network is capable of reducing the spectrum scarcity problem of the wireless networks. Looking at the scarcity of available bandwidth, and the high growth in the number of communication devices in recent times, cognitive radio technology has proven to be a promising technology for the days to come. The application of Game Theory in cognitive radio networks has been visible in recent research works. However, only limited literature is available in which possibilities of applying the game-theory based approaches for the challenging task of channel assignment in cognitive radio wireless sensor are available in the literature. It is understood that the crux of the solution to the problem of scheming games for allocation of the channel is centered on the selection of the utility function in order to increase the efficiency of the channel allocation algorithm. Accordingly, the study regarding the influence of several utility functions on the performance of the corresponding channel allocation algorithm is important. Such a study enables designers to arrive at the optimal utility function to be used in game-theory based channel allocation algorithms, and the same is explored to the best extent, in this paper. The detailed procedure of allocating channels to all the contending nodes through game-based channel allocation has been discussed in this paper. Moreover, the performance of six different utility functions proposed which can be used for channel allocation using game theory has been evaluated for respective performances through MATLAB-based simulations.