Reference: http://en.wikipedia.org/wiki/Tit_for_tat

On homework 2, we were asked to consider the Prisoner’s Dilemma where it was played twice, and both players knew that the game was to be placed twice. The optimal solution for both players was to confess both games. Now, what would happen if the players were told that the game would go on for an unknown number of times, and then against a larger pool of players? That is to say, there will be a pool of 2^m players, who will each play eachother for an unknown number of rounds. Since the players cannot reason about the last game first, they must use forward logic to try and predict what the best move is.

There are two choices the players can make on the first round. They can either confess or not confess. If played only once, confessing is clearly the optimal strategy. But, since the game will most likely be played again, and more than once, the players might consider a different strategy. An effective strategy for this type of game is called Tit for Tat. The rules are simple. A player will not confess unless otherwise provoked (his opponent confessed). A player is quick to forgive other players. That is to say, he will forgive an opponent who does not confess.

Now, consider two players playing against eachother. Player A uses Tit for Tat, while Player B will always confess. Against player B, player A will lose initially, and then always confess. Thus, Player A will be slightly behind. However, if player A plays against an opponent who is also playing Tit for Tat, both players will always not confess, leaving each player with a substantially less penalty then if each confessed.

As described in the link above, the Tit for Tat player will always come out ahead in such a game. The results of such a game, however, are quite surprising. Using such a method changes the Nash Equilibrium from always (Confess, Confess) to (Not Confess, Not Confess). Thus, depending on the desired outcome, whoever is running the game should choose which details to tell the players and which to not. For instance, if the players are 2 criminals wanted for a crime, it is in the interest of the Police to tell them that they will only have 1 chance. If, on the other hand, the criminals know that they will multiple chances to confess, or multiple charges to confess to, it would be in the best interest of the criminals to not confess and see what happens, and carry the result into the next round. But, this is contingent on the fact that the criminals cannot now how many times the game will be played. If it is known, they will always confess.