game-theory1
Aditya K
India, Pakistan and Game Theory
This article originally appeared in centreright.in. CRI content has now been subsumed in swarajyamag.com. The views expressed here are personal and do not necessarily reflect those of the editors of swarajyamag.com

This is what the Times of India reports –

India will retaliate massively even if Pakistan uses tactical nuclear weapons against it. With Pakistan developing “tactical” nuclear warheads, that is, miniaturizing its weapons to be carried on short-range missiles, India will protect its security interests by retaliating to a “smaller” tactical attack in exactly the same manner as it would respond to a “big” strategic attack.

Articulating Indian nuclear policy in this regard for the first time, Shyam Saran, convener of the National Security Advisory Board, said, “India will not be the first to use nuclear weapons, but if it is attacked with such weapons, it would engage in nuclear retaliation which will be massive and designed to inflict unacceptable damage on its adversary. The label on a nuclear weapon used for attacking India, strategic or tactical, is irrelevant from the Indian perspective.” This is significant, because Saran was placing on record India’s official nuclear posture with the full concurrence of the highest levels of nuclear policymakers in New Delhi.

That gets me to talk a bit about some game theory in this context. I will not assume much knowledge about game theory. And I will try to keep the jargon out as much as possible.

One of the first things to do in analyzing this game is going backwards. Now, given that India has declared that its response would be the same irrespective of what kind of nuclear weapon is used – small or large, means that Pakistan, in the event that it decides to use the nuclear weapons, is strictly better off in inflicting maximum damage to India. The reason is simple. No matter what’s the strength of its weapon, the damage in return that it’s going to face is constant. So, it’s only fair to assume that it would be prefer higher damage than lower to India.

Fair enough, so then, we can safely conclude that this statement, if anything, has ensured that if Pakistan ever uses nuclear weapons against India, it will be the biggest possible attack it can. So, in that sense, it seems rather odd that India should have said this.

When would it have been a good statement to make? – To create some uncertainty for Pakistan. What’s the use of uncertainty? We will see that later. But minus uncertainty, this statement can only harm India, as highlighted above.

But then, all this could be a talk in the air. The real question is Will Pakistan ever use nuclear weapons against India? I don’t believe we can answer this question. I also don’t believe that most of those who do answer that question have any real insight about it. Given that the answer to this question is binary, essentially, a random answer is going to be correct with a 50% probability. And that’s a mighty high chance for a guess.

Why do I think that we can’t answer this question? It’s because we know for sure that if Pakistan is as crazy as they sound then they are very likely to attack on slightest of provocation. But what if it’s a fully rational player? That is a player who only maximizes his total benefit and is very shrewd so to say.

Let’s make some very simple and maybe realistic assumptions. Suppose the strength of the two militaries is such that in a conventional war India will have an upper hand. Also, in a nuclear war, due its sheer size, Pakistan cannot wipe India off the map but India can. Lastly, whether crazy or not, the Pakistani state does derive immense pleasure by harming India. So, a fully rational Pakistani state, will not want to go on a conventional war with India. Neither would it want to have a nuclear war with India. But it would want to harm India in some way.

That’s essentially the behaviour that distinguishes the crazy Pakistani elements from rational. The crazy ones do want a nuclear conflict with India, for whatever reasons. The only way they can have such a conflict is by being provoked by India.

Now observe how India would respond. Suppose India believes that Pakistan is a rational state. And suppose the rational Pakistan state carries out 26/11. Then, India’s optimal response is to go all-out against Pakistan. But, if India believes that, with some probability, Pakistan is a crazy state. Then, in all likelihood, India’s response is likely to be quite meek, except in one case that will be mentioned below.

Now, let’s go back to Pakistan. Suppose Pakistan is crazy. Then nobody can do anything about it! They will act according to their will. But suppose it is rational. Even then, given India’s response, it’s best for them to pretend to be the crazy guy.

This is a very key point. The crux is, irrespective of whether Pakistan is rational or crazy, the rational Pakistan will act like crazy to cause confusion for India. That way they can also harm India and avoid a stronger response by India. That is why; the rational Pakistan will always involve itself in acts like 26/11 just so that it looks crazy even though it might not be.

Now go back to India. We know that whenever Pakistan claims to be crazy and carries out operations like 26/11 it is quite likely to be the rational Pakistan acting like crazy and is most likely not crazy. But then, what do we do? What’s the outcome of this game?

And here comes the masterful insight in game theory by Ronald Coase. It’s called the Coase Conjecture. (As an interesting trivia, Coase had a Coase theorem and a Coase conjecture. It turned out that the theorem was false but the conjecture was true.) The gist of Coase conjecture is the following

In a 2-player game, suppose the nature of 1 player is known and there is a some uncertainty (NO MATTER HOW SMALL) about the nature of the other player, then the outcome of the game would be the one most preferred by the player on whose side there’s some uncertainty.

This was a stunning insight by Coase which has been proved many times in various contexts. In the game like the game between India and Pakistan, that of reputation, the Coase conjecture holds. India’s type is known to be rational. We have openly declared ourselves to be rational. And just apply Coase conjecture to our situation.

The outcome will always be in Pakistan’s favour. It has always been and unless something dramatic happens it will always be. The thing about Coase is that no matter how small the chance of the other player is being crazy; once you have revealed your nature the outcome will always be in the other person’s favour!

It is obvious that India comes across as more rational than Pakistan. So it is very hard for India to pull off being as crazy as Pakistan. But then, here are some states, that I think, can invoke some uncertainty about their position and not lose the game –

US

China

Israel

Germany

Coase conjecture is exactly the reason why India cannot be rational all the time and hope that Pakistan reciprocates. The only way India can hope to match Pakistan in this strategic battle is by acting like it. Changing reputation cannot happen overnight. But it’s when you have the chances to change them that you have to take them. 26/11 was a chance we didn’t take.

Some bit of game theory can be very useful, unless you’re an economist PM singing His Master’s Voice. The future, in that case, is something I shudder to think about.