It is undeniably the best time to be alone in human history. If you are sitting immobile on your couch with a phone under your thumb you have infinite information, infinite conversation partners, infinite movies, infinite games, infinite music, infinite video, infinite takes, infinite porn, infinite ragebait propaganda (whatever floats your boat) available for free or for at most a nominal subscription.

And yet despite this abundance, people consistently report being unhappy. We have fewer friends, participate less in public life, care less about our neighbors or our countrymen, feel that life outside of our phones is slowly but surely evaporating, and that our phones are a poor substitute that is slowly killing us all.

So if everyone is unhappy with the current situation, why don’t we just stop? Why don’t we all just go outside?

You guessed it. Equilibria! If nobody outside is doing the thing you want to do, you can’t do it. If nobody gets off their couch, then nobody is doing the thing you want to do. As everyone’s couch gets more entertaining, it can make everyone worse off!

Here’s the graph. We’ll get into the model details for you to nitpick in a sec, but first let me describe the basic behavior. The X-axis here is “How fun it is to be on my phone on my couch.” Don’t worry about the units yet. What we see is that as it becomes more fun to stay in, everyone gets less happy, until you reach a threshold where almost everyone has abandoned the outside world (the gooner singularity) and then everything gradually gets better again as couch living continues to improve and the Children of Men apocalypse outside no longer bothers you.

Ok now for the details for you to nitpick. I assume:

• There is a range of extroversion/introversion in the population. I model this as a coefficient that balances your utility between being with people and being alone. For the graph above I assume the population values of extroversion are distributed as a Beta(3,3) because it’s a nice normalish curve, and makes a nice sigmoid, but any distribution gives you the same conclusion.
• The value of doing things with other people is linear in the number of people doing it. You might object that you only need a small minimum number of people doing a thing to be happy, e.g. once you have enough people for a pickup game of soccer, you don’t really benefit from more. We’ll get to that later. For now assume that this is a niche interest or a small community where the number of people doing it still has incremental returns, things like “Are there kids playing in the local park” or “Does your block have a block party.” This also models things that require a very large amount of effort to organize that few people are willing to do, so you need a large amount of people choosing to invest in your community to get just a few willing to put in the hours, things like “Does your grade school have an active cub scout troop” or “Are there community choirs nearby.” At minimum, the density of people willing to do the thing determines how far you have to drive to do the thing, and how much of a pain it is to do.

This makes each agent’s payoff αn for going outside, where α is their extroversion and n the number of people outside, and (1- α)β for staying in, where β is how fun their phone is, and they choose whichever they like better. One more thing:

• I’m starting the simulation at full participation. This is appropriate to model the gradual decline of community over time, but you get even more depressing results if you start with low participation like we saw after covid. Even ignoring the fact that 0 is an absorbing state, the gradual growth of the group often fails to attract the next most extroverted member, and stalls out well below the best case equilibrium. In an infinite continuous model this wouldn’t be a problem, but the real world has finite integer people who sometimes doom a group by dropping out or never joining.

These assumptions produce that graph, which you can view as an evolution of society over time. As the couch experience improves, marginally introverted people drop out of the community, which reduces the value of the community to everyone else, which causes even more people to drop out. In this fashion the level of community activity drops below what most people want, and everyone ends up less happy.

What happens if we cap the benefit of other people instead of making it fully linear? Maybe you live in NYC, and there are so many people around that the fraction of them that go outside is immaterial to you because there will always be enough. Maybe you’re interested mainly in football, and it’s so popular that the stadium will still fill up even if 80% of the population are hikikomori.

Here’s another graph where the benefit of other people caps out at 50% of them going outside. The situation is much better! Your couch can be pretty great before the activity starts seriously dying off. But again, just like before, once it reaches that critical threshold, average happiness gets worse for a bit before it gets better again in the world of only shut-ins.

So the moral of the story is, to avoid isolation and depression, move to a big city, pick popular hobbies, and if someone asks you to go caroling this Christmas, go even if you don’t want to, because it will make the experience better for everyone else.

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