Power allocation plays a vital role in coordinating interference between Device-to-Device (D2D) and cellular communications, and when power allocation meets simultaneous wireless information and power transfer (SWIPT), the energy efficiency of D2D communications can be significantly improved. While numerous research studies have been conducted on D2D power allocation, most of these studies do not take the presence of SWIPT into consideration. Toward a remedy for this issue, we investigate the problem of D2D power allocation with SWIPT power-splitting architecture, and address it by establishing a novel game-theoretic model. Two power allocation mechanisms are proposed to simultaneously allocate transmit power and choose power splitting ratio for D2D communications. We also develop two pricing strategies for the proposed power allocation mechanisms based on the social utility (sum utility of both D2D and cellular communications) maximization. Simulation results validate theoretical analyses and the effectiveness of the proposed mechanisms. In particular, we find through performance comparisons that our developed pricing strategies are light-weighted and energy-efficient, and the distributed power allocation mechanism is responsive to the mobility of D2D users.