We investigate a set of non-cooperative radio resource management games in a Gaussian interference channel, where the receivers are equipped with two stage Successive Interference Cancellers (SIC). In these games users decide on their transmission power, rate and Interference Canceling (IC) strategy. A one-shot game, as well as two-stage variants, where either rate, or IC and rate, are decided in the second stage, are considered. We characterize the equilibria of the games and establish a relationship between the equilibria of the one shot and two-stage games. Postponing the rate decision to a second stage stabilizes the game in a region where no pure strategy Nash Equilibrium exists for the one-shot game. Further postponing the IC decision to a second stage stabilizes the game completely, an equilibrium exists in all network configurations. We simulate a 2-pair device-to-device network where these games are used for radio resource management. The regions where the one-shot game is unstable have a considerable probability, leading to a considerable outage probability. By staging the game, such outage can be mitigated, or removed altogether.