Be Generous

What can Game Theory tell us about relationships?

Be Generous

Two people get caught for a crime and are separated from each other, but the police need them to testify in order to put them behind bars. They are sentenced as follows:

1. If you both testify, you'll each get 1 year in prison
2. If you both rat on each other, you'll each get 3 years in prison
3. If one gives testimony and the other is a rat, then the rat goes free and the other gets 2 years.

Both of these criminals are smart, but they are also assholes and so only act in self interest. As such, each one rats on the other in the hopes of getting 0 years in prison, resulting in them getting 3 years. But this is the worst outcome for both of them, if they cooperated and gave testimony they would have got away with 1 year in prison instead.

What I've described is a famous problem from Game Theory called a Prisoner's Dilemma. You might remember it from school or the Beautiful Mind. Something lesser known about this game are the many variations of it, and their solutions, but I'll come back to this in a second.

I read Ray Dalio's book, Principles, some time ago and something that came up repeatedly was "what makes good relationships" and "how you should be with people". These two questions are obviously related and underpin much of the satisfaction we get in life but how do you come to an answer? It might be obvious to say "be nice" but is there any way to probe this with logic or do we just have to lean on our subjective faculties? Literature and poetry provide us with a rich account for subjective reasons to be nice, or be mean, or be nothing at all but I thought I'd take a look at what Game Theory can tell us. Obviously the Prisoner's Dilemma and it's variations aren't perfectly applicable to the scenarios that you'll find yourself in, but they give you an extra lens to make decisions through.

The two variations of the game that I want to talk about are the finite and infinite iterated Prisoner's Dilemma. In the finite Dilemma both players play the game over and over again, remembering what the other party did each time and both parties know how many times they will play ahead of time, for instance 10 games. I akin this to the shorter term relationships you might have in life. The people that come and go and that you often need for something, a means to an end. In the infinite Dilemma, the game is repeatedly played, but this time both parties have no clue how long they''ll play together. I akin this game to the close and lifelong relationship's you'll have, the people in your life that aren't going anywhere.

In the finite Dilemma, you can induct backwards from the last game to arrive at a solution. On the last round, both parties want to rat because there will be no retaliation after that. Both of them know that the other person is thinking this way and so rat one game earlier to try get ahead and so on. It's easy to see how this ends up with them ratting on each other from the begininning. In relationships  that you think won't last long or that you use as an opportunity to rise some kind of status ladder, you usually get what you wish for. Relationships that are viewed as a means to an end end up being nothing at all because both parties are playing a zero sum game. Zero sum games are everywhere and while it's easy to get caught up in them they usually suck and are detrimental to the development of everyone involved. Approaching relationships with a long-term and positive sum attitude on the other hand is far better for the soul.

The infinite Dilemma is a little more complicated as there is no analytical solution. Instead you can pit different strategies against each other over and over again and see how they fair in this "virtual setting", usually called a Monte Carlo simulation. An America political scientist named Robert Axelrod once held a competition that people could enter with strategies and see who's fairs the best. Various strategies were tried and the one that faired the best was extremely simple. The winning strategy was to start with cooperation, and only rat if in the previous round the other player had ratted. This is called the "tit-for-tat" strategy but interestingly the strategy faired even better when an element of "forgiveness" was used, that is every now and then, even when you get ratted on to cooperate in the next game anyway.

How do these stupid games apply to my life? Aim to play infinitely iterated games that are positive sum as much as possible. It aligns the incentives of everyone who plays and keeps you honest. Life is a lot more fun when you aren't keeping a tally of favours you've done for your friends and vice versa. Be generous and forgiving to people you love, and cut out status seeking zero sum players from your life where possible. Thankfully I've experienced this generosity from many people. People have taken huge risks to hire me, help me and teach me things with no benefit in mind and sometimes even an obvious loss. Hopefully I surprised them.