Game Theory, Nash Equilibrium, Pareto’s optimal, Kashmir problem

“I want to stress that it is only the people of Kashmir who can decide the future of Kashmir. It is not that we have merely said that to the United Nations and to the people of Kashmir; it is our conviction and one that is borne out by the policy that we have pursued, not only in Kashmir but every where.”

-Nehru, Prime minister of India

India before independence consisted of parts ruled by British government, and princely states. Post-independence India was partitioned into two nations- Muslim dominated Pakistan and Hindu dominated India. Princely states were given option to join either of these nations or if they wanted, to remain independent. Jammu and Kashmir was one such princely state, which wanted to remain independent, it was Muslim dominated state ruled by Hindu ruler Hari Singh. Founder of Pakistan Jinnah claimed that Kashmir should go to Pakistan being a Muslim majority state, Indian Prime minister did not oppose it, so Kashmir could have gone to Pakistan but some political developments prevented that.

Muslims of Kashmir were not happy with Hari Singh; they found a leader in Sheikh Abdullah. Indian Prime minister Nehru too was not happy with Hari Singh and was friendly with Sheikh Abdullah. Both Sheikh Abdullah and Nehru did not like founder of Pakistan M A Jinnah. This set ground for what is called in Game theory as Peace War Game.

nehru jinnah

Without going into details of history of Kashmir, suffice to say Kashmir got divided between India and Pakistan. Some parts went to Pakistan like Gilgit, Baltistan and Azad Kashmir; remaining parts like Kashmir Valley, Jammu and Ladakh remained with India. Today both claim whole of Kashmir belongs to them and this according to them is solution to Kashmir problem.

In game theory there are two important concepts- Nash Equilibrium and Pareto’s optimal.

Pareto’s optimal is an economic state where resources are allocated in the most efficient manner i.e. where one party’s situation cannot be improved without making another party’s situation worse. Pareto efficiency does not imply equality or fairness. The final allocation decision cannot be improved upon, given a limited amount of resources, without causing harm to one of the participants.

Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after considering an opponent’s choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies.


Coming back to Kashmir, Pareto’s optimal can be reached if both India and Pakistan sit together and resolve Kashmir issue. Both countries made efforts to resolve it on negotiation table.

First effort was made when UN intervened and asked both India and Pakistan to hold plebiscite and let Kashmiris decide their future. But for that to happen both countries had to withdraw their armies, but that did not happen and plebiscite never took place.

Second effort was made when Indian Prime Minister Lal Bahadur Shastri and Pakistani President Ayub Khan signed agreement at Tashkent. Again issue could not be resolved.


Third attempt was made when prime ministers of both countries – Indira Gandhi and Bhutto signed Shimla agreement and decided to solve problem mutually. Shimla agreement was soon forgotten.


“If we want to normalize relations between Pakistan and India and bring harmony to the region, the Kashmir dispute will have to be resolved peacefully through a dialogue, on the basis of the aspirations of the Kashmiri people.”

-Pervez Musharraf, ex- Army head and President of Pakistan.

Fourth attempt was made when President of Pakistan Musharraf met Indian Prime Minister Vajpayee. Again talks failed.


Pareto’s optimal cannot be reached because neither politicians nor army is interested in resolution of Kashmir issue; also both players don’t know what optimal solution can be.

Nash equilibrium on the other hand is tit for tat game, and better alternative to Pareto’s optimal, since jingoism keeps both army and public busy. Since optimal solution cannot be found, Nash equilibrium is the only alternative. Also if one player goes for war, the other player has no option but to go for war.

So far I have talked about only two players; actually this game has other players also like citizens of Kashmir, political parties etc.

Earlier there was one more player- China. China believed that some part of Kashmir belonged to them, which they call as Aksai Chin. Instead for going for Nash Equilibrium or Pareto’s optimal, China decided to play game differently.


Nehru was friendly with China and signed treaty called Panchasheel (non-aggression treaty) treaty with China. Nehru also gave lectures on universal peace at various forums. China under Mao and Zhou Enlai did not believe in ideas of Nehru. They tolerated Nehru for some time and then decided to teach him a lesson. They suddenly attacked India and defeated Indian army. They occupied parts of India. Their intention was to take back Aksai Chin and humiliate Nehru. They were successful in both.

They also grabbed few more parts of Kashmir from Pakistan called Trans Karakoram tract. With this they declared that they had resolved their part of Kashmir problem, now dispute was only between India and Pakistan.







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