Bryan Caplan  

Insomnia and Multiple Equilibria

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I was in a bad equilibrium last night. I felt a little agitated when I went to bed, which made it a little hard to fall asleep, which made me more agitated, and which made it even harder to sleep... Long story short: I only slept for three hours, and felt like a zombie most of the day.

During my few lucid moments, it occurred to me that my problem was an odd example of what economists call multiple equilibria. There were two stable situations: One in which I felt calm and slept well, and another in which I felt agitated and slept poorly. Usually, of course, multiple equilibria involve multiple people; but any time there is more than one stable configuration, the concept applies.

Another example: Back when I took tests instead of giving them, I usually stayed calm and did well. But occasionally I got very nervous and did poorly. Once you're nervous, it's hard to do well; and if you're not doing well, it only makes you more nervous.

Given the existence of multiple equilibria, what determines which one prevails? Well, if I could fully answer that, I would have slept like a baby. But here's where I'd start:

1. It's hard to quickly make big changes. I can nudge my mood, but I can't instantly calm down when I'm feeling very agitated. If I'm on the border between sleep and insomnia, telling myself, "Calm down, everything will be fine," usually works. Last night, that just didn't cut it.

(Here's a self-serving interpretation, but that doesn't make it wrong: I'm bad at self-deception. If I tried telling myself stories to make myself feel better, I'd just scoff at myself).

2. Some equilibria are more focal than others. Most nights, it doesn't even occur to me than I might have trouble sleeping. So I'm in the good equilibrium by default, and it takes an unusually event to raise doubts about what's going to happen.

Have you got any other intra-personal applications of the multiple equilibria concept? Any thoughts on how to get to the good equilibrium and stay there?


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COMMENTS (17 to date)
Patrick writes:

Ever toy around with bio-feedback? Granted, lots of variables; however, take a stab (maybe heartbeat rate) and monitor that continuously with alerts above a certain rate.

Cortisol levels sound like a better metric, and it looks like JHU (at least) is working on one.

Theoretically, with feedback you can prevent falling off the wrong sides of your local maxima.

Two words, Bryan: sleeping pills.

HispanicPundit writes:

Good sex does it for me. Puts me to sleep everytime.

Hannes Edinger writes:

I'm seriously worried that just because I read this post, I will have a horrible sleep. Albeit, I AM living in the bush in northern Alberta... where (contrary to popular belief) it can be very hot and humid and we live in tiny muggy dorms. Anything for a buck.

Daily (rigorous) exercise certainly stabilizes almost all of my equilibria.

Eric Crampton writes:

There's no sense in trying to sleep if agitated. Go play some Civ for a couple of hours and try again.

Unit writes:

I get up and eat. I use this trick in many other situations as well: headaches, digestion problems, etc...

caveat bettor writes:

I never look at the clock. Also, I do something recreational, like lounge comfortably, and maybe watch mediocre television or read a mediocre book. I'm usually asleep in under 2 hours.

Les writes:

I read this blog because I'm interested in economics, not your self-indulgent personal problems and navel-gazing.

So, if you have a personal problem write to Dear Abby or Ann Landers, and spare me from your selfish whining.

Jody writes:

I take the equilibrium I'm in and adjust other actions to ensure the equilibrium is a good one.

For instance, on those nights when I realize I have insomnia, I'll get out of bed, go downstairs, and start working on whatever I think is most important for the following day.

Normally after a few hours, I'm exhausted and can fall straight asleep.

Then if I happen to oversleep by an hour or two (or am a bit of a zombie because I had to get up), that's ok, as I already got the most important work for the day done.

liberty writes:

This is interesting. I don't think the comments so far have touched on your main point about equilibria, and feedback which drives the push toward one or the other equilibrium.

There is a positive feedback loop which you indicate, and presumably a critical point which separates the two equilibria. Perhaps a multiplier effect that feeds non-linearly on the fear of not sleeping, compounding the problem until the critical point is reached.

Other fears and compulsions work the same way. Worrying that one is too fat they may eat more to make themselves feel better. Insecurity can make one act funny or interpret people's reactions as negative, feeding the insecurity. Psychological feedback is fairly common. There might be an interesting paper hidden in there about this feedback, equilibria and critical point.

Mark Bahner writes:

"Two words, Bryan: sleeping pills."

A personal story, minus some details.

I virtually never sleep all the way through the night. I always wake up at least once. Tried Rozarem. Didn't work at all. Tried Lunesta. Worked great, but a change in insurers boosted the cost from $70 per 30 pills (expensive enough) to something like $140 per 30 pills.

So my doctor suggested Ambien CR (controlled release). Worked great, and cost $50 for 30 pills. Slept through the night for the first time in years (except the very few times I'd taken Lunesta). It was a very deep, refreshing sleep.

Another thing is that I take naps in the afternoon. I began to find that I would awaken from afternoon naps startled (like someone had shouted at me and shaken me).

Then I started experiencing blood pressure surges as I tried to get to sleep at night.

To make a long story short, I ended up in an emergency room. (Two, actually.) And in the second emergency room, any time I tried to sleep (even though I had slept only 2 hours in the last 30) my blood pressure would soar, and my head would ache. I was given painkillers, but that didn't work. Then I was given Clonazepam, which did work.

My take on the whole situation (I'm not a doctor, and I don't think my doctors agree) is that there is something in my autonomic nervous system that wants me to wake up during the night.

Taking that Ambien CR over-road my autonomic nervous system and put me to sleep throughout the night. But my autonomic nervous system responded by stronger and stronger attempts to keep me from falling asleep. (Again, that's my take. I don't think my doctors agree.)

Needless to say, this was an unpleasant experience. So I recommend caution with sleeping pills...even if they seem to work like a dream, so to speak. I especially recommend caution about long-term use of sleeping pills. Even a week or two, and even if there is nothing in the medical literature that suggests that any negative reactions you might have are from the pills you are taking.

P.S. Please note that I'm recommending caution regarding sleeping pills (especially regarding long-term use), not abstinence.

Zen meditation or contemplative prayer (take your pick).

Both help you to become more mindful of your current state, and thus to make small adjustments to your unstable equilibrium before you get way out of whack.

I wish I practiced this more.

Scott Wentland writes:

Prof. Caplan,

I've had sleeping problems off and on my whole life, and I have some advice to avoid multiple equilibria. The (psychological) key is to cope with a day (or two) of low sleep. Utilize caffine in small, spread out doses throughout the day. Try to push off tasks that require reading or a lot of thinking to the next day, and do more manual things. Go to bed early that night, and you'll likely be so tired that you shouldn't have trouble sleeping (esp. if you fought off the urg to nap).

Once you've learned how to cope with one day on low sleep, and resumed your normal sleep schedule, you'll have the psychological edge on the insomnia anxiety. You'll be able to say to yourself (honestly, not tricking yourself!) that one day or so of low sleep is doable, and it'll allow you to be suffiently tired the next night to get enough sleep and be right back on schedule. This usually calms the anxiety for me. It sounds odd, but you can turn low sleep nights into the cure for insomnia problems and sleep the whole night through the following night.

Also, if you can't sleep, don't fight for hours on end. Just get up and do some reading and things you won't be able to do well when you're tired. Getting stuff done when you're supposed to be sleeping is at least a consulation, and it will probably reduce some anxiety about you day of low sleep ahead of you. Since you got some work done at night, slacking the following day is justified.

Now, instead of multiple equilibria, when you have a lot of trouble getting to sleep, you jump to only one other equilibrium (which is what I just described).

Insonomist writes:

The trick is to commit yourself to the bad equilibrium. Next time you find yourself spiraling downward, get out of the bed and say "Since I'm not going to get any sleep tonight, I might as well get some work done" and start working.

After a while the fact that I am using my time productively relives my anxiety, relaxes me and before I know it, my eyes are shutting themselves.

Kat writes:

The only way I manage to get out of the sleepless agitation is to force myself to take my mind off it and onto something else... playing a fast-paced game that takes up my attention, or scrolling through RSS feeds without pausing so I can just barely keep up.

Also, since my agitation usually comes from a disturbing internal monologue, if I can crowd it out by repeating something over and over in my mind, yanking myself back to the repeated thing when I notice my thoughts drift, I can eventually bore myself back to sleep, breaking the loop.

(Other intra-personal equilibria: I can awaken after a full night unusually groggy, and choose to stay in bed a little longer, which makes me feel more and more lethargic, but at every individual point staying in bed seems the best choice... or I can wake up less groggy, start moving around, and become more refreshed as I become more active.)

Larry writes:

I'm often able to switch off by adjusting my breathing to match that of my sleeping spouse. Those breaths are long and slow, a little quicker on the inhale than the exhale. It can take a few minutes...

patri friedman writes:

classic example of a feedback loop. I suggest a weak sleeping pill, like 2.5mg ambien. You will feel it working, and that will relax you, but it is weak enough to not screw up your sleep much.

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