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Two Person, Zero Sum game Explains Indo-Pak Tensions

In light of the recent Uri attack and following surgical strike, the age old India-Pakistan conflict has once again broken headlines. It is no secret that the two nations have been feuding over Kashmir and other issues since their independence in 1947. A Eurasia Review article by Subrata Kumar Mitra analyses why the India-Pakistan Dialogue needs to be reconceptualised along the lines of “Principle Negotiations.” The article is linked here.

The author displays India and Pakistan’s options of war and peace and their respective payoffs in a two person, zero sum game. Here, if India and Pakistan both choose to maintain peace, both countries receive a payoff of 8. On the other hand, if both countries choose war, each receives a payoff of 4. Finally, if India chooses peace and Pakistan chooses war, India receives a payoff of 0 while Pakistan receives a payoff of 10 (which can represent complete occupation of Kashmir). This game is symmetric, so the symmetric opposite would occur if Pakistan chooses peace and India chooses war. The table is reproduced below.


In this game, the Nash equilibrium output is for both countries to choose war. Through each countries eyes, choosing the peace operation could have yield a payoff of 0 or 8, whereas war could yield either a 4 or 10. Given a choice between 0 and 4, any rational player would choose 4 (war). Hence, Pakistan and india repeatedly choose their Nash equilibrium option of war and receive payoffs of 4, even though both choosing peace would be the optimal choice. As we have learned in class, the Nash equilibrium option is not necessarily the most beneficial option for players in a game. It is interesting to note that this two person zero sum game is also representative of the US-USSR relations at the peak of the cold war.

The author points out that adding an additional player, China, though complicates the game, gives a more realistic image of the payoffs and risks for India and Pakistan. Because of there recent lives lost in the Uri attack and surgical strike, I felt this article was relevant to discuss. The author shows how materials we learned in class about game theory are relevant in how governments and armies operate. It is interesting to see the terms and examples we hear about in lecture being applied to real world problems.

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October 2016