The 'Game' of Defence spendings

I recently read news that Donald Trump denounced Obama era nuclear deal (New START treaty) during his call with Putin. This deal, signed between US & Russia in 2010, limits the number of nuclear warheads deployed by both countries. It led me to think about the bigger game that I had learnt in my Game Theory class.

Basics first:

The above is a very crude and basic payoff matrix for simplicity:

• 2 countries- India & Pakistan
• 2 strategies that each country may follow: Spend on Defence & don’t spend on defence

The payoffs of India are depicted in blue, while the payoffs of Pakistan are in red. Boxes in the bottom right of the cells depict the 4 possibilities.

• In possibility 1, both the countries decide to spend heavily on their defence. Since a large portion of the budget is allocated to defence spendings, it leaves lesser room for more productive public expenditure like health, education, poverty eradication, etc. Both the countries would tend to have tensed relations given that their counterpart is spending heavily on defence. Hence they both would have negative pay offs (Payoffs: India -10, Pakistan -10)
• In possibility 2, India decides to spend on defence while Pakistan abstains from spending. In such a case, Pakistan is at risk of being strong-armed by India in critical matters because of India’s greater arms strength. In the situation of war, Pakistan will be at a severe risk of loss of life and property (Payoffs: India 12, Pakistan -20).
• In possibility 3, Pakistan decides to spend on defence while India abstains from spending. This case is similar to the previous one and the payoffs will be exactly opposite (Payoffs: India -20, Pakistan 12).
• In possibility 4, both the countries abstain from spending. Thus, they are both able to spend on productive public utilities. Both would benefit in such a case (Payoffs India and Pakistan: 10 each).

Concept of Dominant strategy

Looking from India’s point of view,

• If Pakistan is spending on defence – India’s payoff, if it doesn’t spend, is -20 while if it spends, it’s -10
• If Pakistan is not spending on defence – India’s payoff, if it doesn’t spend is 10, while if it spends, it’s 12

Therefore, as seen above, for any given strategy of Pakistan, India’s best strategy (also called the dominant strategy) is to spend on defence.

The same holds true for Pakistan.

Hence, the result is that both the countries end up spending heavily on defence, which might not be the best scenario for both the countries. However, at this point, no country has the incentive to change its strategy. Although, we can clearly see from the table that both the countries are better off if they both abstain from spending.

Note: The above is just a basic structure. In reality, things are much more complex. For instance,

• No. of countries to be considered are much more than 1. There might be other forces too at play, like terrorist activities.
• The no. of strategies available are also many more than 1

It is interesting to note that the defence expenditure of India is ~70K crores and it is consistently increasing year after year despite all the peace treaties that it has. This also affects our balance of trade position adversely which has a direct impact on the foreign exchange rates. (That is why I am happy with the Make in India initiative for defence sector). 

To put this spending into perspective, India’s budgeted spending in 2016 on Housing and Poverty alleviation sector was 5.4K Crores, while that on agriculture and farmer welfare was 36K crore.

Does anyone really gain from Defence?
Yes. The biggest beneficiaries of such sour relations are the developed countries that manufacture and supply defence equipment. USA’s share of global exports in the defence sector is 31% while that of Russia is 27% as per a study by Stockholm International Peace Research Institute. Hence, they have the incentive not to control the arm’s race.

But if US and Russia start spending on their own defence, they will face the same situation as explained above, i.e., both spend and both lose. Then why denounce the nuclear pact?
This is because even if US and Russia both start spending on their own defence, they won’t be at a loss. Other countries, which have hostile relations with them, would also have to spend on their defence for their safety. And so will the enemies of enemies and so on and so forth. This will lead to an arms race in a number of countries across the globe and this will benefit both USA and Russia since they are the biggest exporters of defence equipment!