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Nash Equilibrium, India, Pakistan
|by Gaurang Bhatt, MD|
Two collaborating crooks have robbed a bank and the police are holding them on the basis of some circumstantial evidence, but have no clear basis for conviction. The authorities hold them in separate cells and threaten each one by telling him, that the other is on the verge of cooperating to turn state's evidence and likely to go free, while he will get life imprisonment. Both the detainees are smart professional criminals and know that there is no real proof. Both know that if they refuse to squeal, they will escape with at most a six-month sentence and subsequently enjoy their ill-gotten gains without fear or hindrance. Their dilemma is the lack of faith in each other and the severe punishment that the non-squealer must face if the other one saves skin by squealing. If both confess, they get ten years. Both are aware of all these facts including the length of sentences and know the superior benefits of keeping mum, but unsure of what the other will do. Their dilemma has a clear dominant strategy for a single game and that is to turn state's evidence. If the game is played repeatedly with no clearly defined number of encounters, then cooperation between the crooks is the best strategy. Here maybe the genetic basis of the evolution of cooperation in diverse life forms.
India and Pakistan cannot alter their geographical proximity and are destined to play the reiterated game of Prisoners' Dilemma. Unfortunately Pakistan has chosen to consistently defect and ignore the larger numbers of Moslems of India, while pursuing its fanatical obsession with Kashmir. This strategy can work only in so far as the other party does not have the means to permanently silence the potential defector and there is a higher authority with the wherewithal to impose a punitive sentence. The United States is in that position and thus Pakistan abases itself to this new Khalif, while India is hesitant to anger him.
There are other situations in which there is no dominant strategy and the choice of the best strategy by one player is dependent on the choice of strategy by the other player. One way is to pre-announce the choice by one player and make it known that he is willing to make an unpredictable and irrational choice and stick to it at any cost in the hope of persuading the opposite player to behave prudently and avoid unacceptable destruction. This is like the American teenager game of chicken, where two drivers approach each other for a head on collision and the one who swerves is the chicken. The daredevil pulls off his steering wheel and chucks it out of his car in full view of the opponent, making him aware that he has neither the intention nor the ability to swerve and it would be prudent for the opponent to turn chicken, if he wishes to avoid disaster. USA under Nixon attempted this strategy with the Soviet Union during the Vietnam War.
Pakistan has used this strategy by threatening to use nuclear weapons first, if faced with any unspecified but critically dangerous threat and India has used the Assured Destruction, Mutual or probably that of Pakistan as the deterring defense. The fault in this approach is that it leaves Pakistan free to infiltrate terrorists into India and use salami tactics to pare off India, slice by slice under the aegis of America, like Shikhandi wounding Bhishma. It is imperative that India, take a leaf out of the book of the United States, by clearly announcing that any terrorism will meet with a limited but devastating conventional retaliation over Pakistan occupied Kashmir, from which the terrorists enter India and which India believes is illegally occupied by Pakistan. Granted India does not have Israel's clout to proceed in utter disregard of American wishes, but it would put Pakistan, America and the world on notice that its patience is wearing thin and it will not tolerate the empty braggadocio of this third rate weak bully of a failed state, like Pakistan. This picking of the strategy tailored to combat and neutralize that of the opponent leads to a situation where neither player benefits by alteration and is called a Nash Equilibrium, for which he got the Nobel Prize.
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