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In this paper, the authors 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. They 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, they 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.
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