Nash equilibrium

Labor history in the making

pnrj current events, inequality, market failure, politics, public policy , , , , , ,

Oct 24 JDN 2459512

To say that these are not ordinary times would be a grave understatement. I don’t need to tell you all the ways that this interminable pandemic has changed the lives of people all around the world.

But one in particular is of notice to economists: Labor in the United States is fighting back.

Quit rates are at historic highs. Over 100,000 workers in a variety of industries are simultaneously on strike, ranging from farmworkers to nurses and freelance writers to university lecturers.

After decades of quiescence to ever-worsening working conditions, it seems that finally American workers are mad as hell and not gonna take it anymore.

It’s about time, frankly. The real question is why it took this long. Working conditions in the US have been systematically worse than the rest of the First World since at least the 1980s. It was substantially easier to get the leave I needed to attend my own wedding—in the US—after starting work in the UK than it would have been at the same kind of job in the US, because UK law requires employers to grant leave from the day they start work, while US federal law and the law in many states doesn’t require leave at all for anyone—not even people who are sick or recently gave birth.

So, why did it happen now? What changed? The pandemic threw our lives into turmoil, that much is true. But it didn’t fundamentally change the power imbalance between workers and employers. Why was that enough?

I think I know why. The shock from the pandemic didn’t have to be enough to actually change people’s minds about striking—it merely had to be enough to convince people that others would show up. It wasn’t the first-order intention “I want to strike” that changed; it was the second-order belief “Other people want to strike too”.

For a labor strike is a coordination game par excellence. If 1 person strikes, they get fired and replaced. If 2 or 3 or 10 strike, most likely the same thing. But if 10,000 strike? If 100,000 strike? Suddenly corporations have no choice but to give in.

The most important question on your mind when you are deciding whether or not to strike is not, “Do I hate my job?” but “Will my co-workers have my back?”.

Coordination games exhibit a very fascinating—and still not well-understood—phenomenon known as Schelling points. People will typically latch onto certain seemingly-arbitrary features of their choices, and do so well enough that simply having such a focal point can radically increase the level of successful coordination.

I believe that the pandemic shock was just such a Schelling point. It didn’t change most people’s working conditions all that much: though I can see why nurses in particular would be upset, it’s not clear to me that being a university lecturer is much worse now than it was a year ago. But what the pandemic did do was change everyone’s working conditions, all at once. It was a sudden shock toward work dissatisfaction that applied to almost the entire workforce.

Thus, many people who were previously on the fence about striking were driven over the edge—and then this in turn made others willing to take the leap as well, suddenly confident that they would not be acting alone.

Another important feature of the pandemic shock was that it took away a lot of what people had left to lose. Consider the two following games.

Game A: You and 100 other people each separately, without communicating, decide to choose X or Y. If you all choose X, you each get $20. But if even one of you chooses Y, then everyone who chooses Y gets $1 but everyone who chooses X gets nothing.

Game B: Same as the above, except that if anyone chooses Y, everyone who chooses Y also gets nothing.

Game A is tricky, isn’t it? You want to choose X, and you’d be best off if everyone did. But can you really trust 100 other people to all choose X? Maybe you should take the safe bet and choose Y—but then, they’re thinking the same way.


Game B, on the other hand, is painfully easy: Choose X. Obviously choose X. There’s no downside, and potentially a big upside.

In terms of game theory, both games have the same two Nash equilibria: All-X and All-Y. But in the second game, I made all-X also a weak dominant strategy equilibrium, and that made all the difference.

We could run these games in the lab, and I’m pretty sure I know what we’d find: In game A, most people choose X, but some people don’t, and if you repeat the game more and more people choose Y. But in game B, almost everyone chooses X and keeps on choosing X. Maybe they don’t get unanimity every time, but they probably do get it most of the time—because why wouldn’t you choose X? (These are testable hypotheses! I could in fact run this experiment! Maybe I should?)

It’s hard to say at this point how effective these strikes will be. Surely there will be some concessions won—there are far too many workers striking for them all to get absolutely nothing. But it remains uncertain whether the concessions will be small, token changes just to break up the strikes, or serious, substantive restructuring of how work is done in the United States.

If the latter sounds overly optimistic, consider that this is basically what happened in the New Deal. Those massive—and massively successful—reforms were not generated out of nowhere; they were the result of the economic crisis of the Great Depression and substantial pressure by organized labor. We may yet see a second New Deal (a Green New Deal?) in the 2020s if labor organizations can continue putting the pressure on.

The most important thing in making such a grand effort possible is believing that it’s possible—only if enough people believe it can happen will enough people take the risk and put in the effort to make it happen. Apathy and cynicism are the most powerful weapons of the status quo.


We are witnessing history in the making. Let’s make it in the right direction.

The Race to the Bottom is not inevitable

pnrj development economics, ethics, inequality, macroeconomics, market failure, public policy , , , , , , , , , , , , , , , , , , , ,

Jul 19 JDN 2459050

The race to the bottom is a common result of competition, between firms, between states, or even between countries. One firm finds a way to cut corners and reduce costs, then lowers their price to undercut others; then soon every firm is cutting those same corners. Or one country decides to weaken their regulations in order to attraction more business; then soon every other country has to weaken their regulations as well.

Let’s first consider individual firms. Suppose that you run a business, and you are an upstanding, ethical person. You want to treat your employees, your customers, and your community well. You have high labor standards, you exceed the requirements of environmental regulations, and you make a high-quality product at a reasonable price for a moderate profit.

Then, a competitor appears. The owner of this company is not so ethical. They exploit their workers, perhaps even stealing their wages. They flaunt environmental regulations. They make shoddy products. All of this allows them to make their products for a lower price than yours.

Suppose that most customers can’t tell the difference between your product and theirs. What will happen? They will stop buying yours, because it’s more expensive. What do you do then?

You could simply go out of business. But that doesn’t really solve anything. Probably you’ll be forced to lower your standards. You’ll treat your workers worse, pollute more, reduce product quality. You may not do so as much as the other company, but you’ll have to do it some in order to get the price down low enough to still compete. And your profits will be lower than theirs as a result.

Far better would be for the government to step in and punish that other business for breaking the rules—or if what they’re doing is technically legal, change the rules so that it’s not anymore. Then you could continue to produce high-quality products with fair labor standards and good environmental sustainability.

But there are some problems with this. First, consider this from the point of view of a regulator, who is being lobbied by both companies. Your company asks for higher standards to improve product quality while protecting workers and the environment. But theirs claims that these higher standards will push them out of business. Who will they believe?

In fact, it may be worse than that: Suppose we’ve already settled into an equilibrium where all the firms have low standards. In that case, all the lobbyists will be saying that regulations need to be kept weak, lest the whole industry fail.

But in fact there’s no reason to think that stricter regulations would actually destroy the whole industry. Firm owners are used to thinking in terms of fixed competitors: They act in response to what competitors do. And in many cases it’s actually true that if just one firm tried to raise their standards, they would be outcompeted and go out of business. This does not mean that if all firms were forced to raise their standards, the industry would collapse. In fact, it’s much more likely that stricter regulations would only moderately reduce output and profits, if imposed consistently across the whole industry.

To see why, let’s consider a very simple model, a Bertrand competition game. There are two firms, A and B. Each can either use process H, producing a product of high quality with high labor standards and good sustainability, or use process L, producing a product of low quality with low labor standards and poor sustainability. Process H costs $100 per unit, process L costs $50 per unit. Customers can’t tell the difference, so they will buy whichever product is offered at the lowest price. Let’s say you are in charge of firm A. You choose which process to use, and set your price. At the same time, firm B chooses a process and sets their price.

Suppose choose to use process H. The lowest possible price you could charge to still make a profit would be a price of $101 (ignoring cents; let’s say customers also ignore them, which might be true!).

But firm B could choose process L, and then set a price of $100. They can charge just one dollar less than you charge for their product, but their cost is only $50, so now they are making a large profit—and you get nothing.

So you are forced to lower your standards, in order to match their price. You could try to undercut them at a price of $100, but in the long run that’s a bad idea, since eventually you’ll both be driven to charging a price of 51 and making only a very small profit. And there’s a way to stop them from undercutting you, which is to offer a price-matching guarantee; you can tell your customers that if they see a lower price from firm B than what you’re offering, you’ll match it for them. Then firm B has no incentive to try to undercut you, and you can maintain a stable equilibrium at a price of $100. You have been forced to used process L even though you know it is worse, because any attempt to unilaterally deviate from that industry norm would result in your company going bankrupt.

But now suppose the government comes in and mandates that all firms use process H, and they really enforce this rule so that no firm wants to try to break it. Then you’d want to raise the price, but you wouldn’t necessarily have to raise it all that much. Even $101 would be enough to ensure some profit, and you could even maintain your current profits by raising the price up to $150. In reality the result would probably be somewhere in between those two, depending on the elasticity of demand; so perhaps you end up charging $125 and make half the profit you did before.

Even though the new regulation raised costs all the way up to the current price, they did not result in collapsing the industry; because the rule was enforced uniformly, all firms were able to raise their standards and also raise their prices. This is what we should typically expect to happen; so any time someone claims that a new regulation will “destroy the industry” we should be very skeptical of that claim. (It’s not impossible; for instance, a regulation mandating that all fast food workers be paid $200 per hour would surely collapse the fast food industry. But it’s very unlikely that anyone would seriously propose a regulation like that.)

So as long as you have a strong government in place, you can escape the race to the bottom. But then we must consider international competition: What if other countries have weaker regulations, and so firms want to move their production to those other countries?

Well, a small country may actually be forced to lower their standards in order to compete. I’m not sure there’s much that Taiwan or Singapore could do to enforce higher labor standards. If Taiwan decided to tighten all their labor regulations, firms might just move their production to Indonesia or Vietnam. Then again, monthly incomes in Taiwan, once adjusted for currency exchange rates, are considerably higher than those in Vietnam. Indeed, wages in Taiwan aren’t much lower than wages in the US. So apparently Taiwan has some power to control their own labor standards—perhaps due to their highly educated population and strong industrial infrastructure.

However, a large country like the US or China absolutely has more power than that. If the US wants to enforce stricter labor standards, they can simply impose tariffs on countries that don’t. Actually there are many free-trade rules in place precisely to reduce that power, because it can be easily abused in the service of protectionism.

Perhaps these rules go too far; while I agree with the concern about protectionism, I definitely think we should be doing more to enforce penalties for forced labor, for instance. But this is not the result of too little international governance—if anything it is the result of too much. Our free trade agreements are astonishingly binding, even on the most powerful countries (China has successfully sued the United States under WTO rules!). I wish only that our human rights charters were anywhere near as well enforced.

This means that the race to the bottom is not the inevitable result of competition between firms or even between countries. When it occurs, it is the result of particular policy regimes nationally or internationally. We can make better rules.

The first step may be to stop listening to the people who say that any change will “destroy the industry” because they are unable (or unwilling?) to understand how uniformly-imposed rules differ from unilateral deviations from industry norms.

The game theory of holidays

pnrj cognitive science, core principles , , , , , , , ,

Dec 25, JDN 2457748

When this post goes live, it will be Christmas; so I felt I should make the topic somehow involve the subject of Christmas, or holidays in general.

I decided I would pull back for as much perspective as possible, and ask this question: Why do we have holidays in the first place?

All human cultures have holidays, but not the same ones. Cultures with a lot of mutual contact will tend to synchronize their holidays temporally, but still often preserve wildly different rituals on those same holidays. Yes, we celebrate “Christmas” in both the US and in Austria; but I think they are baffled by the Elf on the Shelf and I know that I find the Krampus bizarre and terrifying.

Most cultures from temperate climates have some sort of celebration around the winter solstice, probably because this is an ecologically important time for us. Our food production is about to get much, much lower, so we’d better make sure we have sufficient quantities stored. (In an era of globalization and processed food that lasts for months, this is less important, of course.) But they aren’t the same celebration, and they generally aren’t exactly on the solstice.

What is a holiday, anyway? We all get off work, we visit our families, and we go through a series of ritualized actions with some sort of symbolic cultural meaning. Why do we do this?

First, why not work all year round? Wouldn’t that be more efficient? Well, no, because human beings are subject to exhaustion. We need to rest at least sometimes.

Well, why not simply have each person rest whenever they need to? Well, how do we know they need to? Do we just take their word for it? People might exaggerate their need for rest in order to shirk their duties and free-ride on the work of others.

It would help if we could have pre-scheduled rest times, to remove individual discretion.

Should we have these at the same time for everyone, or at different times for each person?

Well, from the perspective of efficiency, different times for each person would probably make the most sense. We could trade off work in shifts that way, and ensure production keeps moving. So why don’t we do that?
Well, now we get to the game theory part. Do you want to be the only one who gets today off? Or do you want other people to get today off as well?

You probably want other people to be off work today as well, at least your family and friends so that you can spend time with them. In fact, this is probably more important to you than having any particular day off.

We can write this as a normal-form game. Suppose we have four days to choose from, 1 through 4, and two people, who can each decide which day to take off, or they can not take a day off at all. They each get a payoff of 1 if they take the same day off, 0 if they take different days off, and -1 if they don’t take a day off at all. This is our resulting payoff matrix:

1 2 3 4 None
1 1/1 0/0 0/0 0/0 0/-1
2 0/0 1/1 0/0 0/0 0/-1
3 0/0 0/0 1/1 0/0 0/-1
4 0/0 0/0 0/0 1/1 0/-1
None -1/0 -1/0 -1/0 -1/0 -1/-1

 

It’s pretty obvious that each person will take some day off. But which day? How do they decide that?
This is what we call a coordination game; there are many possible equilibria to choose from, and the payoffs are highest if people can somehow coordinate their behavior.

If they can actually coordinate directly, it’s simple; one person should just suggest a day, and since the other one is indifferent, they have no reason not to agree to that day. From that point forward, they have coordinated on a equilibrium (a Nash equilibrium, in point of fact).

But suppose they can’t talk to each other, or suppose there aren’t two people to coordinate but dozens, or hundreds—or even thousands, once you include all the interlocking social networks. How could they find a way to coordinate on the same day?

They need something more intuitive, some “obvious” choice that they can call upon that they hope everyone else will as well. Even if they can’t communicate, as long as they can observe whether their coordination has succeeded or failed they can try to set these “obvious” choices by successive trial and error.

The result is what we call a Schelling point; players converge on this equilibrium not because there’s actually anything better about it, but because it seems obvious and they expect everyone else to think it will also seem obvious.

This is what I think is happening with holidays. Yes, we make up stories to justify them, or sometimes even have genuine reasons for them (Independence Day actually makes sense being on July 4, for instance), but the ultimate reason why we have a holiday on one day rather than other is that we had to have it some time, and this was a way of breaking the deadlock and finally setting a date.

In fact, weekends are probably a more optimal solution to this coordination problem than holidays, because human beings need rest on a fairly regular basis, not just every few months. Holiday seasons now serve more as an opportunity to have long vacations that allow travel, rather than as a rest between work days. But even those we had to originally justify as a matter of religion: Jews would not work on Saturday, Christians would not work on Sunday, so together we will not work on Saturday or Sunday. The logic here is hardly impeccable (why not make it religion-specific, for example?), but it was enough to give us a Schelling point.

This makes me wonder about what it would take to create a new holiday. How could we actually get people to celebrate Darwin Day or Sagan Day on a large scale, for example? Darwin and Sagan are both a lot more worth celebrating than most of the people who get holidays—Columbus especially leaps to mind. But even among those of us who really love Darwin and Sagan, these are sort of half-hearted celebrations that never attain the same status as Easter, much less Thanksgiving or Christmas.

I’d also like to secularize—or at least ecumenicalize—the winter solstice celebration. Christianity shouldn’t have a monopoly on what is really something like a human universal, or at least a “humans who live in temperate climates” universal. It really isn’t Christmas anyway; most of what we do is celebrating Yule, compounded by a modern expression in mass consumption that is thoroughly borne of modern capitalism. We have no reason to think Jesus was actually born in December, much less on the 25th. But that’s around the time when lots of other celebrations were going on anyway, and it’s much easier to convince people that they should change the name of their holiday than that they should stop celebrating it and start celebrating something else—I think precisely because that still preserves the Schelling point.

Creating holidays has obviously been done before—indeed it is literally the only way holidays ever come into existence. But part of their structure seems to be that the more transparent the reasons for choosing that date and those rituals, the more empty and insincere the holiday seems. Once you admit that this is an arbitrary choice meant to converge an equilibrium, it stops seeming like a good choice anymore.

Now, if we could find dates and rituals that really had good reasons behind them, we could probably escape that; but I’m not entirely sure we can. We can use Darwin’s birthday—but why not the first edition publication of On the Origin of Species? And Darwin himself is really that important, but why Sagan Day and not Einstein Day or Niels Bohr Day… and so on? The winter solstice itself is a very powerful choice; its deep astronomical and ecological significance might actually make it a strong enough attractor to defeat all contenders. But what do we do on the winter solstice celebration? What rituals best capture the feelings we are trying to express, and how do we defend those rituals against criticism and competition?

In the long run, I think what usually happens is that people just sort of start doing something, and eventually enough people are doing it that it becomes a tradition. Maybe it always feels awkward and insincere at first. Maybe you have to be prepared for it to change into something radically different as the decades roll on.

This year the winter solstice is on December 21st. I think I’ll be lighting a candle and gazing into the night sky, reflecting on our place in the universe. Unless you’re reading this on Patreon, by the time this goes live, you’ll have missed it; but you can try later, or maybe next year.

In fifty years all the cool kids will be doing it, I’m sure.