Games Nations Play: A Game Theoretic Analysis of the Strategic Relations between India and Pakistan

Games Nations Play: A Game Theoretic Analysis of the Strategic Relations between India and Pakistan

Competition with India has made Pakistan’s military stronger than other national institutions and independent of civilian control. This reduces the overall welfare of both countries, a situation which would be avoided if both parties to co-operated.

By Kriti Mahajan

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The constructivist approach to history argues that the security practices of India and Pakistan “evolve with every interaction that shapes the norms of identities of the constituent states”. Thus, in the light of increased cross-border firing, the strategic actions of India and Pakistan can be analyzed through a repeated tit-for-tat prisoner’s dilemma. The prisoner’s dilemma illustrates the Nash equilibrium where rational individuals make sub-optimal decisions based on the assumption of non-cooperation by the other parties, even though everyone would be better off if all concerned parties co-operated. In the classic prisoner’s dilemma, there are two prisoners, placed in two different prison cells, who are offered the same deal by a public prosecutor for a crime they committed together. They both have two strategies – confessing or keep quiet – which results in the following payoff matrix:

As can be seen, collectively, the best strategy for both would be to keep quiet as it results in the least damaging outcome. This would be the optimal strategy. However, given the assumption by both prisoners that the other will rat them out, both of them confess – resulting in an outcome which will cause maximum collective damage. This outcome represents Nash equilibrium.

Now, let us apply the aforementioned concept to the strategic interaction between India and Pakistan. Consider the following payoff matrix where numbers 1 to 4 are the ordinal ranks assigned to the payoffs of each strategy, with 1 being the least favored payoff and 4 being the most favored payoff:

Now consider that both in India and Pakistan, the domestic narrative of each country constructs the other as ‘the enemy’ (the reasons for which are beyond the scope of this article). Thus, inaction by the incumbent government in the face of aggression by the other country is perceived as “cowering down”. This results in the loss of domestic political capital for the inactive government while the aggressor gains domestic political capital.

For example, General Ayub Khan (the then-president of Pakistan), Zulfikar Ali Bhutto and Nawaz Sharif gained political capital in the run up to the 1965, 1971 and the Kargil war respectively but lost political capital after losing of each of them. Conversely, in India, Lal Bahadur Shastri, Indira Gandhi and Atal Bihaari Vajpayee gained political capital in in aftermath of the 1965, 1971 and the Kargil war respectively, given India’s victory in each war. However, after the signing of the Tashkent Treaty (which formally ended the 1965 war between India and Pakistan) – which required cooperation between Ayub Khan and Shastri – and the Simla Acord (1972) -, where Bhutto and Gandhi negotiated– each leader lost political capital because each was seen as “cowering down” to the needs of the other country.

In Pakistan, the loss of political support was so dramatic that in two instances it led to regime change. In the 1960s, Bhutto (to increase his own domestic political capital) claimed that Pakistan had won the 1965 war but Khan had squandered the gains to India at Tashkent. This resulted in Khan being replaced by General Yahya Khan and led to the rise of Bhutto. After the Kargil war, Sharif blamed the loss on the architect of the Kargil war, General Pervez Musharraf, and tried ousting him from his position as army chief. However, in trying to do so Sharif compounded his unpopularity, was charged with high treason and removed from office in a coup.

In India, however, Indira Gandhi’s gain in domestic capital surpassed the decline and India’s victory in the 1971 war Pakistan helped the Indian National Congress  defeat the Left-dominated United Front in West Bengal. More recently, in 2008, post the Mumbai 26/11 attacks, former Prime Minister Manmohan Singh continued to engage with Pakistan diplomatically. He was perceived as being soft on terror, a factor which contributed significantly to the loss of UPA II to the NDA in the 2014 elections.

Thus, the worst outcome for India is when India co-operates and Pakistan doesn’t (1, 4) and vice versa for Pakistan (4,1).

Given that history has proven time and again that the majority of the electorate in each country (spurred by their respective media houses) favors non-cooperation, the greatest gains in political capital are made by indulging in non-cooperative behavior. Hence, Prime Minister Narendra Modi and Sharif have chosen retaliatory military action as their strategy. Given this, the Nash equilibrium is (2, 2). This is a sub-optimal solution for the citizens of both countries as it results in greater spending on military and less investment on consumer goods. For example, competition with India has made Pakistan’s military stronger than other national institutions and independent of civilian control. This reduces the overall welfare of the citizens of both countries, a situation which would be avoided if both parties to co-operated (3, 3).

But the outcome from non-cooperation is only a precursor to a longer-term outcome of potential escalation. India’s strategies must be informed by its beliefs regarding Pakistan’s strategy, which in turn depends on its payoffs from cooperation and non-cooperation. While the Nash equilibrium tells us that escalation of matters will take place between India and Pakistan, the degree of escalation will depend on Pakistan’s payoff from war (probability of winning (P) minus the cost of war (Cp)) and the payoff from backing down (x), as Pakistan is the first mover in this case. Pakistan will indulge in war only if its payoff from war (P- Cp) is greater than the payoff from backing down (x) i.e.

Probability of winning (P) – the cost of war (Cp)> Payoff from backing down (x)

The probability of winning increases with the presence of strong allies, the formal support of the international community, past military spending, and the strength of espionage (proxied by the networks of ISI for Pakistan and RAW for India). The cost of war includes cost of human capital (that is, subjective valuations about the value of human life vis-à-vis that of the state), equipment, war taxes, and losses due to reduction in trade. The payoff from backing down increases as the economic viability of war increases and declines otherwise.

For instance, according to most historians, the 1965 war was the last war that Pakistan had a high probability of winning against India. It had more advanced technologies, better equipment, better NATO-standard training and the support of multiple allies (notably USA and China). India on the other hand was reeling from the loss of the 1962 war with China and was fraught with Naga insurgency, Dravida separatism and an unstable Kashmir.

Presently, the situation is very different. A ‘soft coup’ has been in effect in Pakistan since August 2014 which has strengthened the position of the army vis-à-vis the elected government. Sharif is fast losing domestic political capital, exacerbated by the corruption probe ordered against him by the Supreme Court in connection to the Panama papers. In November, the term of the then Army Chief of Pakistan, Raheel Sharif, concluded and thus all prospective candidates “wanted to exhibit their credentials in terms of their previous and current operations against India”. In addition to the above, non-state actors play a co-operative game with the ISI to destabilize Kashmir, where they may gain significant political capital due to the on-going discontentment with the Indian government in the valley. The last factor reduces the payoff for Pakistan for backing down. The remaining factors provide the aforementioned parties with reason to collude and increase the anti-India rhetoric to gain political capital as this diverts attention from the failure of domestic policy to increase the welfare of the Pakistani people. Such an approach reduces the value of individual human life and liberty vis-à-vis that of the state and thus reduces the cost of war. This increases the payoff from war as compared to the payoff from backing down.

However, the first mover in a bilateral conflict loses international political capital as it is seen as an aggressor who poses a threat to the prevailing world order. Thus, as with the 1965 and 1971 wars, post the Uri attacks Pakistan has faced almost complete international isolation. In conjunction with the persistent growth rate of about 3 per cent, this implies that Pakistan currently lacks the financial capacity to support its threats of war.

Thus, the ‘surgical strikes’ by India will not result in deterrence of counter strikers by Pakistan because, given the inability of Pakistan to participate in full scale war, Pakistan will continue to escalate matters through an increase in the number of encounters along the LoC. Given the aforementioned scenario, the optimal strategy for the India government will be to increase the cost of encounters for Pakistan by a) increasing the capacity for monitoring and self-defense along the LoC for the Indian Army and b) increasing investment in consumer and social goods in Kashmir to build support for the Indian state and thus reduce the discontent which results in individuals becoming enablers of militant actions. Increased military brutality would be ill advised as would increasing the anti-Pakistan rhetoric as both these strategies play into Pakistan’s overall strategy of presenting India as the villain.

A change in the status quo with respect to international relations, however, will require a reexamination of this crisis bargaining scenario.