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In this paper, we look into the channel allocation problem for a non-cooperative cognitive vehicular ad-hoc communication network with multiple communicating pairs distributed spatially apart. An algorithm which can search for all pure Nash Equilibrium (NE) solutions is presented. We study how the number of pure NEs grows when either the size of the network or the number of available channels gets higher. Myopic play of a game, in which the players take turn to choose its best response strategy, is a common approach to obtain one of these NE solutions, if the algorithm converges. However, we found that for myopic play of the game, the probability of convergence to the NE which has the desired best global utility is not guaranteed. We further propose two player ordering schemes to study how the probability of hitting the best global solution among all possible NEs is affected. We find that by allowing the node with the lowest "expected" utility to decide first increases the chance of hitting the NE solution with better utility value.