A Nash equilibrium is a state of equilibrium between two parties in which one only party changing their behavior will not make things better for that party. It will require both parties to change their behavior simultaneously to make things better for both.
It might surprise the reader to know that the author of this blog has had some experience with societal relationships; even some with the opposite gender. My college girlfriend and I started on a good note, and then due to mistakes made with time, things became more complex. Towards the end of our relationship, we settled upon an equilibrium in which we were both rude, uncompromising and unhelpful towards each other. Let me try and explain why this was a Nash equilibrium.
When one of us would feel bad about how things had turned out, and would try to be nicer so as to turn back time and return to how things were, the other would be unaware of such intentions, and only mock the other person for being fake and artificial. This would, of course, anger the person with good intentions, and we would both return to being terrible to each other. Note how one person trying to change their behavior for the better only made things worse for that person (invited accusations of insincerity). This is why this was a (bad) Nash equilibrium. A bad Nash equilibrium is caused by a lack of coordination. If both parties agreed that things had taken a turn for the worse, and that they had to change together for things to become better, there could perhaps be some hope.
I see relationships at bad Nash equilibria all around me. My extended family is often at bad Nash equilibria with one another. Many members of my extended family are not nice to each other during family functions, and one member unilaterally trying to make things better by being nicer or more helpful almost always invites only suspicion or derision from others (“Why is s/he suddenly being so nice? What is the point of this fake gesturing?”) This of course causes that one member to lose steam, and the state of affairs to return to the previous bad Nash equilibrium in which everyone is terrible to each other.
Any way out?
Is there any way out of bad Nash equilibria? One way of course is to tell everyone about your intentions. If you want things to become better between you and your family members, you should tell them that you want to try and become nicer to them so that things may become better with time, and that this bad Nash equilibrium was only hurting everyone. This may convince them to also be nicer to you, and soon things may turn for the better. But is it as easy as that?
The sad news is that two parties being good to each other is not a Nash equilibrium. If you and your friend are good and helpful to each other, and you decide to become inconsiderate and unhelpful while your friend remains good to you, you are of course at an advantage. You can take all the help you need from them, while being rude and dismissive towards them. This is why two people being nice to each other is not a stable state of affairs, as one is always tempted to defect (stop being nice). Similarly, if you and your romantic partner decide to be nicer to one another, as soon as you have an argument in which you try to prove your moral superiority, the person who brings up old issues to prove that they have historically been morally superior to the other will be at a temporary advantage in the argument. This of course causes the other person to bring up other old issues as well to prove their own moral superiority, and soon both parties return to the previous state of bad Nash equilibrium.
Money is always the answer
Is there any hope? I’d like to believe that there is some. If you and your partner are in a bad Nash equilibrium, you need to realize that being good to each other for the long term is a very difficult thing to achieve (it is not a Nash equilibrium), and that a single argument may send things hurtling down towards the bad Nash equilibrium (being terrible to one another). Hence, you need to resolve your old issues if there is to be any hope. But how does one do that? The answer to that is money (and my baniya-ness is only partly the reason why I came up with this explanation).
Suppose there was an incident in the past that causes you both to keep bringing it up and fighting about it. If you both blame each other (and both of you probably are to blame), you are only talking past each other without any hope for reconciliation. What you need to decide is how much both of you are to blame. You may come up with something like you were 7/10 to blame, and you partner was 3/10 to blame (this of course assumes that both of you are still cooperative enough to agree on these numbers). Both of you have concluded that you were more to blame. Now you can decide upon a monetary fine, depending upon your financial condition. Something in the range of ~$50 is reasonable if the issue involved is small, while larger amounts may be appropriate for more serious issues. Suppose you guys decide on a fine of $60. Transfer this amount to your partner. In my experience, this ends the issue then and there. If your partner ever comes up with this issue again in a future argument, you can remind them that you’ve paid your dues, and then they’ll have to switch to another issue in their search for moral superiority. Of course, if you’ve done this for every serious issues that you’ve had, there will be no other issues to go back to, and it will be easier to be nice to one another.
Can you do the same with relatives/co-workers who you are in a bad relationship with? I believe that you can. However, it will be harder to get them to the drawing board to sort these issues out. Your uncle who you’re in a bad Nash equilibrium with may not agree to go out for dinner with you to sort your old issues out. Even if he does agree to this meeting, he may be insulted if you ask him to assess his blame for any of your issues. If you have relatives like that, with whom there is a power differential, realizing that things are not going to get better is the only way out. However, there is hopefully no power differential between you and your partner, and you can mutually agree to sort out your issues using this method.
Perhaps the reason why people are (generally) bad to each other in this world is that being bad to one another is a stable Nash equilibrium, while being good is not. Thus ends my spiel on applying Nash’s rich and complex Game Theory in an overly simplistic way to our daily lives; with some buzzwords wrapped in a platitude.