In the Bitcoin system, large numbers of miners invest massive computing resources in the blockchain mining process in pursuit of Bitcoin rewards, which are comprised of a fixed amount of system-generated new block reward and a variable amount of user-submitted transaction fees. Here, transaction fees serve as the important tuner for the Bitcoin system to define the priorities in users' transaction confirmation. In this paper, we aim to study the priority rule for queueing transactions based on their associated fees, and in turn users' strategies in formulating their fees in the transaction confirmation game. We first establish a full-information game-theoretical model to study users' equilibrium fee decisions; and then discuss three types of Nash equilibria, under which no, all and some users submit transaction fees. Moreover, we conduct empirical studies and design computational experiments to validate our theoretical analysis. The experimental results show that (1) users' fee decisions will be significantly affected by their waiting time; (2) the reduced time costs, instead of transaction values, are the basis for users to evaluate their revenues; (3) longer waiting time and higher unit time cost drive users to submit transaction fees in pursuit of desired priorities; (4) with the required transaction fee increasing, the proportion of fee-submitting users decreases slowly at first followed by a sharp decline, and over-high required fees will make the transaction confirmation game end up with no users submitting fees.