Game Theory: Applying Strategy to Prisoners Dilemma

Intro to strategies for solving Prisoner’s Dilemma

Originally we used Nash Equilibrium to solve for both sequential and simultaneous games. However, there are other methods and strategies for analyzing games. In this blog we will direct our attention to Prisoner’s Dilemma.

An example of Prisoner’s Dilemma is below:

1\2 Cooperate Defect
Cooperate 3,3 -2,6
Defect 6,-2 0,0

The Nash Equilibrium for this game is (Defect, Defect) for a payout of (0,0). This is assuming that both players are rational decision makers and they know each other are rational decision makers. However, in the real world we know that this is not the case. Players can either have advantages or disadvantages. So is it possible that players can end up in different strategy spaces (Cooperate, Cooperation) than (Defect, Defect)?

One possible strategy is providing an incentive or reward. Player 2 can be given the incentive to cooperate rather than defect by means of a suitable reward. On the flip side of this, Player 2 can be deterred from defecting by being threatened. But the reward approach is unsustainable and can create problems. For example, the reward cannot be given before the choice is made otherwise Player 2 can just take the reward and then defect. In addition, if the reward is not credible and just promised, Player 2 can decide to defect.

On other hand, punishment more than often used to solve Prisoner’s Dilemma. However, the threat must be credible and hold weight otherwise the other player will not cooperate. Fear of retaliation can be a very effective tool.

Sports like baseball can illustrate threat of punishment to maintain cooperation. American League batters are more prone to be hit pitches than National League batters. This is due to the fact that American League pitchers do not go up to bat so the threat of punishment doesn’t hold much weight. But National League pitchers have to bat so the fear of retaliation/punishment is more apparent.

Another strategy used in Prisoner’s Dilemma is tit for tat. This is a variation of the eye for an eye rule which says to do unto others as they have done onto you. The strategy cooperates in the first period and from then on copies the other player’s action from the previous period. The founder of the tit for tat strategy listed four principles that must be used in an effective strategy.

  1. Clarity – Tit for tat is clear and simple.
  2. Niceness – It never initiates cheating.
  3. Provocable  – The strategy does not let cheating go unpunished.
  4. Forgiving – It does not hold a grudge for too long and will return to cooperation.

However, a major problem with tit for tat is there is no end. It involves too much provocation and not enough forgiveness. Player 1 would punish Player 2 for defection which would set of the endless cycle. Player 2 would respond to the punishment through retaliation which provokes another punishment from Player 1. Unfortunately we see this occur in Middle Eastern conflicts (Israel vs Palestine). Next time we will continue to look at more ways to achieve cooperation.


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