if . This shows that if , playing C is pareto optimal. Step 2: Suppose that someone has played D previously, then Player j will play D no matter what. Player i's payoff from C : Player i's payoff from D : Since , playing D is optimal. The preceding argument emphasizes that there is no incentive to deviate (no profitable deviation) from the cooperation profile if , and this is true for every subgame. Therefore, the strategy for the infinitely repeated prisoners’ dilemma game is a Subgame Perfect Nash equilibrium. In iterated prisoner's dilemma strategy competitions, grim trigger performs poorly even without noise, and adding signal errors makes it even worse. Its ability to threaten permanent defection gives it a theoretically effective way to sustain trust, but because of its unforgiving nature and the inability to communicate this threat in advance, it performs poorly. Grim trigger in international relations Under the grim trigger in international relations perspective, a nation cooperates only if its partner has never exploited it in the past. Because a nation will refuse to cooperate in all future periods once its partner defects once, the indefinite removal of cooperation becomes the threat that makes such strategy a limiting case. While grim trigger is a limiting case, Folk theorem states that a perfect equilibrium can be made if both nations are patient. Grim trigger in user-network interactions Game theory has recently been used in developing future communications systems, and the user in the user-network interaction game employing the grim trigger strategy is one of such examples. If the grim trigger is decided to be used in the user-network interaction game, the user stays in the network (cooperates) if the network maintains a certain quality, but punishes the network by stopping the interaction and leaving the network as soon as the user finds out the opponent defects. Antoniou et al. explains that “given such a strategy, the network has a stronger incentive to keep the promise given for a certain quality, since it faces the threat of losing its customer forever.” Comparison with other strategies Tit for tat and grim trigger strategies are similar in nature in that both are trigger strategy where a player refuses to defect first if he has the ability to punish the opponent for defecting. The difference, however, is that grim trigger seeks maximal punishment for a single defection while tit for tat