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

Kriti Mahajan is a Junior Research Assistant at Monk Prayogshala, a not-for-profit academic research institution based in Mumbai, India.

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. Consider the following payoff matrix. The 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:

IndiavsPak Equilibrium

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, as rational actors, both Prime Ministers, Narendra Modi and Nawaz Sharif chose to respond through retaliatory military action. Given this, the Nash equilibrium is (2, 2). In a standard IS-LM framework, 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. 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).  The domestic narrative of each country constructs the other as ‘the enemy’. 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. Following the signing of the Tashkent Treaty (which ended the 1965 war between India and Pakistan) General Ayub Khan lost political control over Pakistan and was ousted by the opposition. In India, former Prime Minister Manmohan Singh continued to engage with Pakistan diplomatically post the Mumbai 26/11 attacks. He was perceived as being soft on terror, a factor which has been argued to have 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).

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 in Pakistan’s strategy set, which in turn are contingent on an analysis of Pakistan’s payoffs. While the Nash equilibrium tells us that escalation of matters will take place between India and Pakistan, the degree of escalation is a function of 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.

P – Cp>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.

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. Prime Minister Nawaz 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. The tenure of the current Army Chief Raheel Sharif will conclude by the end of November and all the prospective candidates “want 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 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, post the Uri attacks Pakistan has faced almost complete international isolation. In conjunction with the persistent growth rate of about 3%, 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 as, 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. However, a change in the status quo with respect to international relations will require a reexamination of this crisis bargaining scenario.


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