Gandhian Game Theory

After Seeing the Movie - " A beautiful Mind " for the first time- like most people I had became a fan of the legendary John Nash and his even more legendary "Nash Equilibrium" and had done quite some reading on the same issue by googling him , but I was little kid then who didn't understand the profoundness of Nash's Equilibrium. Then came a day when my grandfather, who was studying Nobel Laureates then , asked me -"Who's this guy John Nash ? Do you know whats so brilliant about his equilibrium that fetched him a Nobel ?" - There Began my Round II of research on John Nash and now being a 3rd year Engineering student - I guess I had matured enough to taste the Whiskey called John Nash and not spit it out saying "It tastes yuck" but let it sink in and make me "high"- and I am still high ....

John Nash's Equilibrium can be best explained using the Prisoner's Dilemma - A classic Game theory problem- Where 2 robbers on way to robbery have been caught by the police trespassing - Now the Police "know" that the robbers were up to a Robbery but they have no proof and can only book them for trespassing. But the Police are smart asses - they decide to turn the 2 robbers against each other to gain proof -They lock each of the robber in separate rooms and offer each of them a deal without letting them communicate with each other - Defect on your partner and we will let you go free without booking you even for trespassing and will screw your partner for the entire robbery.

So Now each of the robber has 2 options:

1.Betray Partner

2.Stay Silent with partner

Plotting this 2 options of the 2 robbers in a matrix form we get 4 scenarios

	B Stays Silent	B Betrays
A Stays Silent	Each serves 6 months	A: 10 years B: goes free
A Betrays	A: goes free B: 10 years	Each serves 5 years

Thinking from Point of view of A : A thinks " Whatever B does my sentence will always be less

if I betray him " because given if B remains silent , A get 0 if he betrays whereas 6 months if he too remains silent and if B betrays him , then if A remains silent then he gets 10 years and if A too betrays he gets only 5 ! So in any case - Mathematically speaking A is better off Betraying B.

But come on - Same is true for B too - B too is always better off betraying A. So as they say in Game theory Jargon - Betraying is the Dominating Strategy for both the players !

Now if you see there are 2 Equilibrium points in the matrix - (Silent,Silent) and (Betray,Betray) -where both get equal term. But (Silent, Silent) is an unstable Equilibrium because when engaged in that equilibrium , there is an "incentive" to change your strategy, your sentence reduces if you change given your opponent doesn't change. The (betray,betray) on other hand is stable equilibrium , because if u change your strategy from there and your opponent doesn't - then u r screwed ! This Stable Equilibrium is known as the "Nash Equilibrium" and it almost accurately captures the essence of natural human behavior and you can predict given such a scenario - its highly likely that the Game will end up at the Nash Equilibrium ! Don't believe that humans can act so stupidly - Nuclear Arms Race during the Coldwar - its Pure Nash Equilibrium in Action !!! Option to USSR and USA being to produce or not to produce nukes !

Now .......lets get back to the title of the Blog - Where Does Gandhi come into picture ?!

Gandhi somewhere down the line realized that - " Nash Equilibrium" which we saw was a very sad place to be in ! Win Win Nash equilibria do exist - but not in the case we were studying ! Gandhi realized that only way of avoiding a "lose-lose Nash Equilibria" is to for someone to take one step backward first ! Lets describe another scenario with help of a pay off matrix to justify Gandhiri

	B is Violent	B is non-Violent
A is Violent	Each gets hurt	A: is unhurt B: gets hurt
A is non-Violent	A: gets hurt B: is unhurt	Each is unhurt

The Dominating Strategy here again is to be violent and hence the Nash Equilibrium is at intersection of dominating Strategies of both players and unfortunately in it both get hurt !

Gandhi ideally wants you to be at the unstable equilibrium where both remain unhurt - but for that someone has to take the 1st step of immediate mathematical irrationality - Gandhi says taking this 1st step though apparently irrational is very important and requires true Courage !

the Courage he says u can only derive when U have truth on your side - Once you have taken the 1st step it causes your Opponent to morally move to the unstable equilibrium . So does Morality and mathematics mix is an open ended debate ? The first step of nonviolent Satyagraha is definitely not supported by Game theory - But one could argue that immediate rationality in being violent is myopic and Satyagraha is your way to support the unstable equilibrium which in the long run is Win win ! Gandhi here is supported by another polymath - Douglas Hofstadter

(whose book- Godel Escher Bach is a must read) - Douglas Hofstadter argues that rationality which ends in lose-lose situation is not rationality at all , hence He defines what he calls "Super Rationality" as a virtue of both players by which they will chose non-violence as their strategy which will get them better results in the end ! So is it morality or super Rationality - I dont know - but I know Gandhi as a man was able to break the "Nash Equilibrium" of pre-independence struggle , where British killed us in Jallianwalla Baugs etc and we killed their officers in return, and shifted the whole dynamics to a "Win-Win" unstable equilibrium and most importantly maintain it ! So cheers to the man who defied Game theory or should I say introduced us to a new Moral Game Theory - Gandhian Game Theory !