Grim Trigger

Grim Trigger is a strategy for the Iterated Prisoner's Dilemma, which takes its name from the extremely harsh punishment it metes out to any participant that fails to cooperate with it. Trigger-response strategies are common in the IPD, and Grim, initially cooperating, reacts to the simplest trigger - a single defection - with the harshest response: defecting in all future rounds.

Grim featured in Axelrod's tournament¹, having been entered by James W. Friedman. There it placed seventh of the fifteen participants. In his analysis of the tournament, Axelrod identified several desirable properties for a winning strategy. Grim meets one of these, falling in the category of 'nice' strategies- where nice is given the precise meaning of not being the first to defect in any given encounter. The top eight consisted of the eight nice strategies, since when paired against each other, a virtuous cycle of consistent mutual cooperation is established.

However, Grim rates poorly for another key property- that of forgiveness. Whilst it shares a trigger with the tournament winner, Tit for Tat, the response by that program to defection only lasts for a single round, and thus an opponent can improve its score (and that of TfT) by resuming cooperation. Grim lacks such forgiveness, which makes it more resilient to random strategies, but is ultimately harmful when paired against more sophisticated strategies that would seek recovery of the more desirable mutual cooperation. Thus Grim found its way to the bottom of the pile of nice strategies: the eighth was a Grim variant that cooperated for ten rounds, before switching to permanent defection if the opponent had failed to cooperate in any of those ten rounds.

A common mistake in modifying Tit for Tat was to make the programs less forgiving to avoid random exploitation, which Grim takes to the logical conclusion of zero forgiveness. Axelrod concluded that being more forgiving of transgressions was the appropriate route- for instance, the Tit for Two Tats program, which will respond with a single defection to a trigger of two sucessive defections, would have placed even higher than Tit for Tat in the tournament.

Nonetheless, Grim can be an appropriate metagame call- if you expect a field of conventional Tit for Tat, you do no worse by playing Grim (due to niceness all round); and if any random programs are introduced, you will probably do better. If however more complicated programs likely to test the waters by throwing out the occasional defection are expected, then TfT or other more forgiving options remain the best choice.