In this paper, we developed a novel Bayesian game theoretic framework to study the coexistence problem between two FD-capable wireless links, where nodes have heterogeneous SIC capabilities. Although the throughput of a single link enhances significantly when operating in the FD mode, the additional caused interference (compared to the HD case) may limit its coexistence with a neighboring link. Our analysis revealed that the SIC capability of each link (which is the type of each player) has a double-threshold structure, i.e., the range of the SIC values can be divided into three regions. When the SIC capability is very good, operating in the FD mode strictly dominates the HD mode, whereas when the SIC capability is very poor, operating in the HD mode strictly dominates the FD mode. When the SIC capability is in the middle region, we derived the conditions on the probability distribution of the types of the other link under which HD (FD) strictly dominates FD (HD). Our conducted experiments corroborated that FD is not always the optimal operation mode when considering an FD enabled wireless network. The optimal mode of a link depends on (i) the external interference it encounters from neighboring links (which is a function of their transmission powers and channel gains) and (ii) its residual self-interference (which is a function of its SIC capability, its transmission power, and its channel gain). Given that the external interference will not be known a priori, a link relies on the probability distribution over the types of the other link in deriving its strategy. Our simulations demonstrated the impact of the residual self-interference and external interference on the received constellation diagram, and hence the BER. Specifically, as both interference types increase, the variance in the received constellation points increases. As future research, we plan to extend the proposed Bayesian game into more than two links, where each link does not know the exact SIC capabilities of the neighboring links. We will also investigate a power control scheme to be used as part of the game, in addition to FD/HD mode selection.