The "grim trigger" strategy is an angle in
game theory, particularly pertaining to infinite
iteration and the
prisoner's dilemma. The idea is to create a
Nash Equilibrium (NE) of the
Pareto Optimal solution through repeating games where there was previously a non-Pareto optimal
dominant strategy.
...a little payoff matrix to refresh you
2,2 0,7
7,0 1,1
The strategy basically goes like this: "Do not confess (
cooperate with me) and we will continue a cooperative tradition to
perpetuity. The payoff for this is 1+1*delta+1*delta^2+...1*delta^n where delta is your discount rate for future payoffs. (remember the lowest score is best in prisoner's dilemma) If you ever confess (cross me) then I will forever punish you by confessing. Period. No forgiveness possible. Assuming you find this to be a
credible threat (a fair assumption unless you have some other information about my personal
discount rate) it is an NE for you to cooperate.