The Game Theory Behind Tit for Tat

Posted on Sunday, January 17, 2021

 People are often heard whispering "Tit for Tat", but reciprocally. Yet, what is the game theory behind Tit for Tat (TFT)? For that, what is TFT? 

TFT is the usual game for two/more individuals or two/more groups. It starts with a situation where one of the teams is given a chance to first act. This act can be of two types, either defection or cooperation. Then the second player acts according to the previous move. The most classic and well-known example is Chess. When white moves its piece, the black always makes a move according to the first. But this is not always right. In chess, if a move doesn't concern you much, you can follow your lead using your strategy without being in a situation where you have to act accordingly. 

However, there is one fascinating game theory called the Prisoner's Dilemma, which uses TFT (and its extensions) very much. It is intricate at first but self-realizing after you allow the logic to play itself. Merrill Flood and Melvin Dresher were the first ones to realise this game. Afterwards, Robert Axelrod influenced this game theory.

Prisoner's Dilemma is a situation concerning the two criminals who are arrested. Let's say A and B are criminals. Just for the sake of game theory, we give both the criminals a chance to get free from charges. Conditions are that A and B are given two choices. These choices are imagined on a ground where both are standing with each other. The options are to either defect/betray the opponent or remain silent. The catch is, they are not allowed to talk or get informed about one another. Rules are as follows,

  • If A betrays B, and B betrays A, both will be charged with two years of the sentence.
  • If A betrays B and B remains silent. Then A will get free, and B will be charged for three years.
  • If B betrays A and A remains silent. Then B will get free, and A will be charged for three years.
  • If neither A nor B defects each other, they get only one year of charge.
This game is often played in analysing society and its next move. But, reading a criminal mind is not that easy.

For instance, A believes that if he defects the B, he will be free. And B at the moment decided to cooperate because B thought it would be in everyone's favour. Hence, on-ground A defected B and B cooperated, so B was defeated and charged for three years. You can analyse the same using replacing B with A. What if they both are willing to cooperate? This is uncertain, because A doesn't know what B has planned, and vice versa. The prisoner's dilemma offers a lot in the study of human minds and social actions.

Let us move to a more realistic example. When two soldiers of contrast political demographics join one another on the battleground to fight. They have two options, either they attack or stay calm. But this is also uncertain. For instance, one soldier wants to cooperate because he(/she) doesn't want to die, but he doubts the second soldier, may he attacks the first. And if that happens, the first one loses. So here comes the TFT. If one soldier shoots the other, then the second one will do the same, so TFT. If the first one cooperates, may the second cooperate or take the lead from the situation and kill the first.

So, it can be seen that the game is impressive. But what is the ideal situation in TFT? Most say that cooperators win most of the game. Only if both of them are rational. But, your every step should be structured using the tactics the opponent used in the last round. Cooperators or defectors, both can be found in society. And game theory suggests you perform, eye to eye, head to head, elbow to elbow, and most crucial peace to peace.

- A.V

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