Game Theory

Introduction

India and Pakistan have been involved in conflict over Kashmir since Independence. It has led to numerous wars and attacks. The relations and wars over Kashmir can be studied using Game Theory. Tit for Tat policy has been practiced by both nations. The pay of for wars for both countries has been changing depending on the context. This context has been based on many parameters – 1. Ally countries – US and China are widely regarded as Pakistan allies. China has been against India due to border issues. USSR has been traditionally supporting India until recently. The situation keeps on changing with changing stance of allies. 2. International support – International communities like UN tries to solve the conflict through negotiations. 3. Military strength – It keeps on changing depending upon development and purchase of weapons on both sides. 4. Resources including financial and others – India has always been in a relatively better position due to more available resources. 5. Leadership of both countries especially of Pakistan (Army Rule) – Army Rulers might perceive war as a more beneficial situation. 6. Public opinion : Both sides have to consider the opinion of citizens of their country

This context keeps on changing. But another important parameter of Nuclear Deterrence was seen during Kargil War.

Indo-Pak Relations: A Game Theoretic Perspective

Kashmir has been the centerpiece for the conflict between India and Pakistan ever since independence. The individual stands of India and Pakistan over Kashmir can best be described as a Prisoner’s Dilemma as shown below. Each country has two options: to either give up its claim over Kashmir (Cooperate) or stick to its claim.

Pakistan
India Cooperate Defect
Cooperate Both countries give up their claims and Kashmir becomes an Independent State. This is the Pareto Optimal solution.(3,3) Pakistan gains control of Kashmir(0,5) Defect India gains control of Kashmir(5,0) Disputes and conflicts in the form of wars, militancy etc(1,1)

If India and Pakistan both give up their respective claims and Kashmir becomes independent, it will be Pareto Optimal since the extra resources spent in wars/conflicts will be saved and this will be the optimal solution from society’s perspective. However, this is a classic case of prisoner’s dilemma where each country sees a higher payoff in defecting or keeping its claim over Kashmir. Hence, both end up not withdrawing their claims and the Nash Equilibrium is one where both have a claim over Kashmir and results in disputes.

Both countries have a dominant strategy in keeping their claim and fighting over Kashmir and hence they have followed this since independence.

Buildup to Kargil War

India and Pakistan had been practicing Tit for Tat strategy for a while before the Kargil War. This means that the players decide their moves depending on what the other player does first. Hence, a defection is followed by a defection to teach the other player a lesson to cooperate.

This started with the Indian Prime Minister, I.K.Gujral and Pakistan premier Nawaz Sharif deciding to cooperate by setting up a direct hot line and a bus service between Lahore and New Delhi.

Then India defected first by conducting a nuclear test in May 1998 under Atal Bihari Vajpayi. Pakistan soon followed with a defection by conducting a nuclear test of its own. This once again led to strained relationships.

The Indian Government then learned from its mistake and decided to cooperate by starting the planned bus service between Lahore and New Delhi. Atal Bihari Vajpayi went on the inaugural run to signal cooperation. Pakistan again responded with positive signals for cooperation.

However, soon after Pakistan decided to defect once again resulting in the Kargil war.

Kargil War: Analysis through Game Theory

Pakistan saw an opportunity to defect since the peace process was going pretty well and India was not expecting an attack. The element of surprise shifted the payoffs in favor of Pakistan attacking India. Hence, infiltration was the best strategy for Pakistan under those circumstances.

However, India was in a better position in terms of military strength and resources and decided to defend its claim. Also, China and US decided to oppose Pakistan’s action which Pakistan might not have foreseen. Also, the extensive media coverage helped in forming a strong international opinion against Pakistan in the war. This eventually led to India’s victory while Pakistan decided to withdraw its forces.

Nuclear deterrence also played a very important role in limiting the war from escalating to a full scale conventional war. This was due to reduced payoffs for a full conventional war which resulted from the threat of using nuclear weapons.

References

1. Game-theoretic Understanding of India-Pakistan Relations, Arvind Gupta, http://www.idsa.in/idsacomments/GametheoreticUnderstandingofIndiaPakistanRelations_agupta_160811 2. Can India and Pakistan mitigate the Prisoner’s