[2][3] The infinitely repeated prisoners’ dilemma is a well-known example for the grim trigger strategy.
In fact, both players are better off to stay silent (cooperate) than to betray the other, so playing (C, C) is the cooperative profile while playing (D, D), also the unique Nash equilibrium in this game, is the punishment profile.
Once the player finds that the opponent has betrayed in the previous game, he will then defect forever.
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.
[6] Under the grim trigger in international relations perspective, a nation cooperates only if its partner has never exploited it in the past.
[9] 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.”[8] 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.