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In this paper, we consider a cognitive radio network where multiple heterogenous secondary users (SUs) compete for transmissions on idle primary channels. We model this as a singleton congestion game, where the probability for an SU to successfully access a channel decreases with the number of SUs selecting the same channel. In particular, we consider player-specific payoffs that depend not only on the shares of the channel but also on different preference constants. Such system can be modeled as a congestion game, and we study the price of anarchy (PoA) for four families of such a game: identical, player-specific symmetric, resource-specific symmetric, and asymmetric games. We characterize the worst-case PoA in terms of the number of SUs and channels, and illustrate the network scenarios under which the worse case performance is reached. We further illustrate the PoA results with two Medium Access Control (MAC) schemes: uniform MAC and slotted Aloha. For both cases, we observe that the average performance of the game equilibrium is better than the worst-case PoA. Our study sheds light on how to design stable systems with smaller efficiency loss of the equilibrium.