Recently, tremendous progress has been made in self-interference cancellation (SIC) techniques that enable a wireless device to transmit and receive data simultaneously on the same frequency channel, a.k.a. in-band full-duplex (FD) communications. Although operating in a FD mode significantly improves the throughput of a single wireless link, it doubles the number of concurrent transmissions, which limits the potential for coexistence between multiple FD-enabled links. In this paper, we consider the problem of concurrent transmissions between two FD-enabled links with different SIC capabilities; each link can operate in either FD or half-duplex (HD) mode. Following a game-theoretic framework, we aim to determine the stable behavior (FD or HD) for the two coexisting links. To achieve this objective, we first analyze a simple normal form game between the two links, which provides some insight into the coexistence problem. It turns out that the outcome of this game depends on two factors: The amount of residual self-interference (due to imperfect SIC) and the external interference from one link on the other. To capture the impact of residual self-interference, we formulate a Bayesian game between two links with heterogeneous SIC capabilities. In this game, each link (player) tries to maximize its throughput while minimizing the transmission power cost. We derive the Bayesian Nash equilibrium for this game. Furthermore, we determine the conditions on the external interference under which no outage occurs at both links. Finally, we conduct simulations and USRP hardware experiments to corroborate our analytical findings.