Game Theory

Topics: Game theory, Prisoner's dilemma, Nash equilibrium Pages: 7 (2157 words) Published: April 6, 2013
Will the Meek inherit the Earth?

“Be still before the Lord and wait patiently for him; do not fret when men succeed in their ways, when they carry out their wicked schemes. Refrain from anger and turn from wrath; do not fret – it leads only to evil. For evil men will be cut off, but those who hope in the Lord will inherit the land. A little while, and the wicked will be no more; though you look for them, they will not be found. But the meek will inherit the land and enjoy great peace.” Psalm 37: 7-11

This essay began with a simple question: When should a person cooperate, and when should a person be selfish, in an ongoing interaction with another person? Should a friend keep providing favours to another friend who never reciprocates? Should a business provide prompt service to another business that is about to be bankrupt?

Is it possible to have “Always Cooperate” as your dominant strategy, no matter what the other person does this is always better? Will such meek be able to survive when they give an open chance to exploiters to keep defecting and gaining? Will the meek inherit the earth?

The world has been preaching moral philosophy and few have been really practicing them. Many quote versus from the Bible and other religious books like above. Some believe that the world is still going on because of some good left in it and others think it is because people have learnt to punish the defectors. Let us study these philosophies in comparison with Prisoners Dilemma & Tit-For-Tat strategy in Game theory.

Game theorists, like gamblers and children, can become addicted to iterated games. Their classic example is the Prisoner’s Dilemma, whose diabolical simplicity has given rise to thousands of scientific publications. Two players are engaged in the game. They have to choose between two options, which we term Cooperate or Defect. If both cooperate, they can earn three points apiece as reward. If both defect, they get only one point each, which is the punishment for failing to join forces. If one player defects while the other cooperates, then the defector receives five points (this is the temptation) while the trusting co-operator receives no points at all (this is the sucker’s payoff). How will the rational player act? By defecting, of course. This is the right choice, no matter what the other player does. Indeed, against a cooperating player, one earns five points by defecting, but only three points for cooperation. Against a defecting player, one earns one point if one also defects, but nothing at all if one cooperates. Hence, Defect is always the best option.

The trouble is that the other player, being rational too, thinks along exactly the same lines. As a result, both players end up with only one point each-two less than mutual cooperation would have produced for each of them.

For most people, this conclusion is not very easy to swallow. Indeed, I am happy to report that in experimental tests players frequently prefer cooperation. In fact, cooperation has such a positive image that defecting makes one feel like a louse. Quite obviously, a good conscience is worth more than the silly difference of a few points.

The provision of public goods and the conditions for participation in collective action are inescapably bound up with attempted solutions to the Prisoner’s Dilemma. For instance, a simple decision about pollution. Do you throw a piece of litter on the ground or not? You like a clean environment, but one piece of litter is not going to make a difference, and who needs a sticky sweet paper in their pocket? But, if everyone makes the same calculation, there will be litter all over the place. Reflections such as this reveal how central the Prisoner’s Dilemma is to social life.

How can there ever be cooperation between competitors in the absence of conscience or constraint? Well, possibly through the prospect of repetition. It is obvious that traders in the habit of defaulting on their...
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