Common knowledge and counter-strikes

Can Game Theory explain how India made the decision to speak out about the surgical strikes its army conducted in Pakistan Occupied Kashmir?


Photo: AFP
Photo: AFP

To speak or not to speak—that must have been the question facing India’s leadership with regard to the recent surgical strikes. Does game theory—the study of decision-making in interdependent situations, i.e. situations in which the outcomes and the pay-offs of a “player” (a person, firm, or country involved in the situation) depend not just on what the player does but also on what others do—offer any answers?

The mathematical model of games defines a game as consisting of a set of players, each with a set of strategies, and a pay-off table specifying the pay-offs, i.e. gains and losses to each player from the adoption of any combination of strategies, one for each player. Game theorists base their analysis on two assumptions.

The first assumption is that players are rational, i.e. they aim to maximize their pay-offs. We will have occasion to return to this rather controversial assumption later in this series. The second assumption holds that the elements of the game (players, strategies, pay-offs) are “common knowledge”, i.e. known to everyone, known to be known, known to be known to be known...ad infinitum. The higher levels of knowledge implied in the assumption can be shown to have immense practical significance through a striking example.

Two people with green eyes can see the colour of the other person’s eyes, not their own. They know the irises can either be brown or green. A good samaritan comes into the room and announces that “at least one of you has green eyes”. Both wait an instant to see if the other will speak, as each would if the other player’s eyes happened to be brown. But since the other person’s eyes are green, both remain silent. The silence leads each to exclaim, “Oh, so I have green eyes!” Note that each player already knows that there is a pair of green eyes in the room. But the samaritan’s announcement has made this information “common knowledge”, i.e. now each player knows that the other player knows there is a pair of green eyes in the room. This triggers their simultaneous epiphany.

News reports confirm that India’s recent surgical strikes in response to militant attacks in Uri may not have been the first, although the details are being contested. The new aspect of this situation is that we have made our retaliation common knowledge by declaring there has been a strike. How does this change the interaction between the “players”—the Pakistani and Indian governments and civil society and the global leadership?

First, the announcement now makes it abundantly clear to India and the world at large that the Pakistan government knows there has been a surgical strike. This makes it incumbent upon Pakistan to respond. Their attempted denial notwithstanding, the stepping up of militant attacks and cross-border firing indicates that the response has begun and will continue.

Second, the avowal is a signal to the Pakistani public and civil society that India’s patience is running thin and it no longer feels the need for “deniability” of its counter-terror operations. This is likely to strike a chord as the people of Pakistan are themselves victims of terrorism.

The declaration and the consequent disapproval of terrorism by world leaders is also a possible tool in the hands of the political elite of Pakistan in their ongoing power struggle with the military and militants. It comes at an opportune time when the present army chief’s tenure is coming to an end. The reported differences between Shahbaz Sharif and the ISI head indicate that the politicians have initiated their moves.

The triggering of a mood against terrorism in Pakistan depends on its people having the impression that India has been a stoic onlooker to past attacks and has acted only when the provocation snowballed to unbearable proportions. In this context, the revelations by the opposition that India has engaged in such strikes in the past damages India’s ability to claim the high ground.

But such revelations were always on the cards when we recall that the announcement also has an impact on one other constituency—the Indian people who are about to vote in a slew of critical state elections. The claim by the government that the Indian Army has recognized its strength for the first time through these strikes is unfortunate and has not helped to lower the political temperature. Similarly, the Prime Minister’s sympathy for the cause of Baloch separatists, expressed from the ramparts of Red Fort, may make India’s alleged involvement common knowledge but it does so to the detriment of our cause in Kashmir.

Finally, the announcement has prompted countries around the world to come out in the open about their stands on cross-border militancy in Kashmir. The support of countries such as the US and Russia, though muted, is welcome. The stonewalling of China, for instance on the declaration of Masood Azhar as a terrorist, is to be expected, given the US’ emerging tilt towards India and China’s alignment with Pakistan. A piquant question facing India’s foreign policy establishment has come into sharp relief: Does India want to become the front line of the superpower tussle between the US and China, a clash in which terrorism is merely one bargaining chip, and the India-Pakistan rivalry a convenient schism? Or will it rely on its traditional strengths—the interwoven fabric of Indian life and the fostering of a dynamic self-serving non-alignment to negotiate the emerging new world order?

The mere declaration of surgical strikes is forcing countries to reveal the colour of their eyes, a fact that the good samaritan would have well anticipated.

Rohit Prasad is a professor at MDI, Gurgaon and author of Blood Red River. Game Sutra is a fortnightly column that uses the lens of game theory to examine matters big and small.

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