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==Iterated Prisoner's Dilemma==

==Iterated Prisoner's Dilemma==

The Iterated Prisoner's dilemma is when the basic game is played multiple times (sometimes infinitely many times). Here, co-operation can be a Nash equilibrium. This requires that each player pays attention to what the other player does on previous "rounds", and punish or reward the other player as appropriate. One of the best strategies in the Iterated Prisoner's dilemma is the "tit for tat" strategy. The "tit for tat" strategy is to cooperate the first time and then on all subsequent times the strategy is to do whatever the opponent did on the turn prior to the one you are on.

The Iterated Prisoner's dilemma is when the basic game is played multiple times (sometimes infinitely many times). Here, co-operation can be a Nash equilibrium. This requires that each player pays attention to what the other player does on previous "rounds", and punish or reward the other player as appropriate.  

 

In 1980 Robert Axelrod put out a call for experts in game theory and computational science to send in algorithms for playing an iterative Prisoner's Dilemma. He proposed to have all submitted algorithms compete in a tournament to see which one was the best. A total of 14 algorithms were submitted, ranging from immensely complicated and computational intensive to extremely simple. The results were published in the Journal of Conflict Resolution and as it turned out the simplest and smallest algorithm won the tournament. It was developed by Anatol Rapoport out of the University of Toronto and it was called "tit for tat". The "tit for tat" strategy is to cooperate the first time and then on all subsequent times the strategy is to do whatever the opponent did on the turn prior to the one you are on. While subsequent algorithms have been developed that can best the "tit for tat" strategy it remains the most computationally efficent. Because of this it has been proposed as the strategy that humans employ in social interactions. 

An additional strategy that is often followed and debated is the "Grim Trigger": that is to say, cooperate until the first defection, and from then on out, defect every turn.  Grim Trigger tends to work only when there is informational exchange.

An additional strategy that is often followed and debated is the "Grim Trigger": that is to say, cooperate until the first defection, and from then on out, defect every turn.  Grim Trigger tends to work only when there is informational exchange.