## Relationships and the Iterated Prisoner’s Dilemma

It was around this time last year that something snapped, and things have never been the same again. Until then, whenever she threw some tantrums, or we had some fight, I’d always give her the benefit of doubt, and unconditionally apologise, and make an effort to bring the relationship back on track. But since then, I don’t feel the same kind of sympathy for her. I don’t feel “paapa” for her like I used to , and have questioned myself several times as to why I even aoplogise, and not expect her to do that.

The optimal strategy for Iterated Prisoner’s Dilemma has been shown to be a strategy called “Tit for tat”. To explain the problem, you play a series of games against an “opponent”, and in each iteration, each of you choose to either “cooperate” or “defect”. For each combination of choices, there is a certain payoff. The payoff looks similar to this, though the exact numbers might be different. In this table, the first value refers to the first player’s payoff and the second represents the second player’s.

 Player 1/ Player 2 Co-operate Defect Co-operate 1 / 1 2 / 0 Defect 0 / 2 0.5/ 0.5

So you play this game several times, and your earnings are totalled. There was a tournament for computer programs playing this game sometime in the 1960s, where the winner was “tit for tat”. According to this strategy, you start by co-operating in the first iteration, and in every successive iteration you copy what your opponent did in the previous iteration. Notice that if both players choose this strategy, both will co-operate in perpetuity, and have identical payoffs.

Relationships can be modelled as an iterated prisoner’s dilemma. You can either choose to be nice to your partner (co-operate) for which you get a steady return, or you can choose to be nasty (defect), in which case you get a superior payoff if your partner continues to be nice. If both of you are nasty simultaneously both of you end up getting inferior payoffs (as shown by the Defect-Defect box in the above matrix).

Early on in the relationship, I was very keen to make things work and did my best to prevent it from falling into any abyss. I played the “Gandhi strategy”, where irrespective of her play, I simply co-operated. The idea there was that whenever she defected, she would feel sympathy for my co-operative position and switch back to co-operate.

So something snapped sometime around this time last year, which led me to change my strategy. I wasn’t going to be Gandhi anymore. I wasn’t going to unconditionally defect, either. I switched to playing tit-for-tat. You can see from the above table that when both players are playing tit-for-tat, you can get into a long (and extremely suboptimal) sequence of defect-defects. And that is what happened to us. We started getting into long sequences of suboptimality, when we would fight way more than what is required to sustain a relationship. Thankfully it never got so bad as to ruin the relationship.

Periodically, both of us would try to break the rut, and try to give the relationship a stimulus. We would play  the co-operate card, and given both of us were playing tit-for-tat we’d be back to normal (Co-operate – Co-operate). Soon we learnt that long defect-defect sequences are bad for both of us, so we would quickly break the strategy and co-operate and get things back on track. We weren’t playing pure tit-for-tat any more. There was a small randomness in our behaviour when we’d suddenly go crazy and defect. In the course of the year, we got formally engaged, and then we got married, and we’ve continued to play this randomized tit-for-tat strategy. And the payoffs have been a roller coaster.

Today I lost it. She randomly pulled out the defect card twice in the course of the day, and that made me go mad. While in earlier circumstances I’d wait a few iterations before I started to defect myself, something snapped today. I pulled out the defect card too. Maybe for the first time ever, I hung up on her. Do I regret it? Perhaps I do. I don’t want to get into a prolonged defect-defect sequence now.

And I hope one of us manages to give the relationship enough of a stimulus in the coming days to put us on a sustained co-operate co-operate path.

## JEE Results

Exactly ten years ago, they used to give a sum total of 3400 ranks for IIT-JEE. Typically, to get an engineering branch at one of the “big 5” IITs you needed to be in the early 2000s or better. Back then, there were ~40 people from Bangalore who made it to the merit list (I’ve forgotten the exact numbers but if I remember right, at least 30 people from Bangalore JOINED some IIT or the other). About 1.2% of all successful candidates back then were from Karnataka (for IIT/JEE purposes Bangalore = Karnataka since there are no other centres in the state).

JEE results for this year came out yesterday. Most of the second page of today’s The New Indian Express is spent in giving footage to people from Bangalore who got a rank. This year, they gave out 13,100 ranks, of which 58 were from Bangalore – 0.5% of all successful candidates. And you have the New Indian Express which puts the headline “City Students crack IIT by the dozen”. Yeah, five dozen out of thirteen kilopeople is worse than three dozen out of three kilopeople. But anyway…

Back in my days, there was one decently established factory and a couple of fledgling factories in Bangalore. The established factory (a small scale industry by national standards) had 100 students, of which over 30 got ranks in the JEE (and about 20 actually joined IIT). Today the same factory has some 500 students. And surely not more than 58 of its students could have cleared the JEE! And then there are several other factories in the city. Don’t know if any of them have done significantly well.