More interesting games than the prisoner’s dilemma

I think game theory is awesome. First of all, it is the most ingeniously named field in the history of thought. Who doesn’t want to study something called “game theory”? Marketing!

Second of all, it forces a student—it certainly forced me—to confront kinds of logic, problem-solving, and epistemological questions that are quite different to the norm. Certainly quite different to the norm elsewhere in economics, at least. It is thinking about thinking, which for a certain type of person is a fun rabbit hole.

Game theory is about how we can try to understand situations in which the outcome of my choice depends also on what you choose. These are situations with strategic interaction. I can’t just pick the thing I like best, as in the standard rational choice model. I have to think about what you want, what you might do, how you might respond, what you think about me, what you think I might do—and you have to think all of those things right back at me. It’s gnarly!

So I saw this at the Browser today:


How often do you see a reference to game theory that isn’t about the prisoner’s dilemma? Very seldom, if ever, I think, and in my opinion game theory is worse for it.

I include in that references to game theory in academic courses too, by the way. I’ve taught game theory for undergraduates many times (in the context of applications to economics), and it’s remarkable how many students come to those classes under the impression that game theory is the prisoner’s dilemma. I don’t think they are wholly to blame for the mistake.

I’m not here to tattle on anyone, but I’ve had smart students show up at game theory class and tell me that game theory is about how you should rat out your friends. Uh oh!

Now, I come not to praise the prisoner’s dilemma, but nor do I want to bury it. First, it swiftly and usefully undermines the notion that decentralized decision-making necessarily leads to mutually beneficial outcomes. Second, as with any simple game, it can be extended and varied in endless ways to tell many rich and useful stories—most obviously by thinking about a repeated prisoner’s dilemma with inducements, rewards, and punishments. Third, it’s a useful parable for a variety of real-world situations.

There are more qualities of the game, of course. For a dive into the depths of what it can teach us, I recommend its entry in the Stanford Encyclopedia of Philosophy.

But here’s the problem: the vanilla prisoner’s dilemma is the least interesting game in game theory. I’m not going to rehash the setup again here (trust me, it’s been done enough). The reason it’s the least interesting game is that the very point of the prisoner’s dilemma is that its setup gives each of the two players in the game a unilateral incentive to make a given choice.

The vanilla prisoner’s dilemma boils down to the smallest variation on the rational choice model. I don’t particularly need to think about what you might do, or what you might be thinking. No matter what you do, one of my options is always better. Yeah, it carries a non-trivial lesson, but to me it just seems so flat. I don’t really get much of a hint of the mind-bending joys of game theory from it. If this is game theory, then game theory isn’t much at all.

And so often, in my experience, students see the vanilla prisoner’s dilemma, see it called game theory, and then move on to something else. Nothing else is being imprinted on them about the example or the field. I think that’s a shame.

So in that spirit I call on those of us who would like to touch on game theory in non-game theory course, or those of us who write game theory into introductory economics texts, to consider showing, instead of or as well as the prisoner’s dilemma, some different interesting games. Here are a few of my suggestions:

  1. The Keynesian beauty contest is another very famous game. I think it is super useful in a classroom setting. It gets very quickly at many of the “big questions” in the study of games and it’s a lot of fun to play and argue about in a group. It also unleashes “One, Two, (Three), Infinity, … : Newspaper and Lab Beauty-Contest Experiments” by Rosemarie Nagel et al, which is one of my all-time favorite papers to teach, especially its peerless appendix.
  2. The centipede game is not a million miles away in spirit from the prisoner’s dilemma, but it is (i) way more fun for students to play in the classroom, and (ii) teaches the power and weirdness of backward induction. Also an introduction to the thorniest problem for the typical game theory student, that “a strategy” is a pre-play complete contingent plan, not an on-the-fly decision. Bonus: the “crazy centipede” variant: what if there’s a tiny chance that my opponent is irrationally cooperative?
  3. Rock-paper-scissors. Seriously. Everyone knows it, and the soul of the concept of Nash equilibrium lives here. So is the distinction between playing a game in real life versus “a strategy” in game theory that I mentioned a second ago in #2. See also Wolfers on the Patriots-Seahawks Super Bowl.
  4. The Hotelling location game. Readily graspable, hugely widely applicable, has a ton of interesting variations, and teaches many of the same lessons as the prisoner’s dilemma. It also opens the door to location problems more generally, which are always fun.

I’m not saying we have to retire the prisoner’s dilemma’s number just yet. But I think we can do a little more when we give our students their first taste of the rich, fun field of game theory.

If you have any thoughts on my game suggestions, do let me know!

The scale of society

As I sit at my desk and look around me, I see a lot more than I could hope to do alone. The computer I’m typing on, the appliances in my kitchen, the coffee in my cup, the books on my shelf, the stores outside my window, the garbage cans outside my back door, the street at the end of the path… there is not a single thing that I would be able to replicate alone.

I don’t know about you, but once I start thinking about the immense web of trade, combination, and connections that make up the world we live in, I know awe. I don’t have the words to describe how the stuff I see around me came to be. It’s alchemy. (This, by the way and for the economists, is why general equilibrium theory blew my mind when I first saw it.)

Trade is an issue ever at the heart of political discourse. This year, Brexit and Trumpism have elevated its urgency in the public discourse. I won’t talk here about any specific trade deal, whose details are seldom clear-cut (see, for example, a short note on TPP from Beat the Press today). I want to instead think about the concept of trade itself. Fundamental to the issue is a deep question: what should be the scale of our society?

If I was alone in the world, I would be done for. If I was very lucky and busted my tail I might be able to Robinson Crusoe myself an existence for a little while. I am fragile: a twisted ankle could mean the difference between life and death.So let’s start by accepting the obvious truth that going it alone is not going to get us anywhere.

What about a few people? I’ll try to build shelter, you see about getting us some food. If you get sick, I have your back. We may rediscover the power of specialization to make us more than proportionately powerful together than apart.

At the level of a person, specialization and trade are simple things. Sure, there is systemic coercion in our lives, but trade, entered into willingly, is nothing more than a little win-win. A little of what I have and a little of what you have and we are both better off than before.

But we are not yet remotely close to building a toaster.

What about a small town? You know, Main Street U.S.A., with a hardware store, a bakery, a soda fountain, an elementary school, a factory. We’re specializing a little more, increasing the scale of our little society. But the scale is not just what we see in our zip code. Already our idyllic picture is cheating a little bit. The goods in the hardware store, the textbooks in the school, the lumber in the houses all took more to produce than our little town can accomplish alone.

When it comes to the stuff you consume, the borders of your society are not the same thing as the scale of your society.

We may also start to see a type of fragility creep in to our world. That factory is maybe not just working to make a thing for our town, but for many towns. Our town is specializing in that thing. We are trading that thing for the other stuff we are using but don’t make. So tell me: what is the scale of this society? And tell me: what happens if the thing our factory makes becomes obsolete?

What about a state? A country? Whole regions may be devoted to banking, or product assembly, or the auto industry, or agriculture, or mining. The scale of society through trade must become huge: a region certainly wants to eat more than just banking services. And, inexorably, now the local risk may not be so local after all. What do we do here? And what do we do when the day comes that we can’t do it anymore?

People’s lives must change with scale too. Adam Smith’s pin factory, where each person has a tiny, repetitive task, is not likely any worker’s idea of a good time. He knew this, and we know this. For most people, though, living alone off of the land in the woods is also likely to get old pretty quickly.

And, in our hypothetical hyper-specialized region, if I want to make my way in life in some other way, I have to cast myself out, to move to a place that does something different. That costs me, physically and psychologically.

Where is the sweet spot?

Would you prefer it if your town, state, or country were closed, forced to be entirely self-sufficient? What would you be willing to sacrifice to make that happen? There is nothing wrong with saying: yes, I would accept fewer things, more expensive things, in exchange for shutting us off from the rest of the world. But in my heart I don’t think this is what anyone wants. I’m not sure that people want to be isolated from the world or from the variety it brings. I think we just want a nice place to live and something to do.

I want a small town, with a Main Street rather than a Wal-Mart, and what unleashes Wal-Mart more than logistics and trade? I love being able to afford more stuff, but I hate that all I have left are strip malls. (I’m only half kidding when I say that better real estate and some interior design would be the cheapest way for Wal-Mart to buy our goodwill.)

From this angle, specialization means drudgery and local risk. From that angle, trade means variety and the freedom to pursue my own path.

Can we square the circle? I’m sure there is a connection between the increasing scale in society and Bowling Alone, but they are not exactly the same. I think that we can find some daylight between them. Maybe we could even find that, down there somewhere, trade and community share more than they seem.

Earlier I said that when I look at the stuff around me I am in awe. I see so much stuff that if you tried to explain it to someone from a few generations ago they would burn you as a witch. But I also see cooperation, community, and interdependence among humanity on a scale I can’t comprehend. Trade is a conception of community too.

If a desire for community is imprinting on politics is as part of the lament against trade, maybe we are not so far from a consensus after all. Maybe I’m overstating the case. But at a minimum, pro-social and pro-trade policies do not need to be seen as mutually exclusive opposites. Delivering both in one package would be a fine trick.

everything & everything & everything – Alberto Roldán

I saw this short film at the Toronto International Film Festival in 2014, and I just found out it’s available to watch on YouTube as part of the Vice Shorts series. It’s by Alberto Roldán, and stars Shane Carruth, the filmmaker behind Primer and Upstream Color.

Here’s a plot summary by an anonymous contributor at IMDb:

The oppressively vapid life of Morgan is forever transformed when a mystical blue pyramid – that inexplicably produces doorknobs – appears in his apartment. What follows is a tale of greed and loss as Morgan builds an impossible, absurd corporate empire of doorknobs.

… uh huh.

It has the same disorienting, abstract qualities of those Carruth films, with an added absurdist streak. Among other things it is about manufacturing, automation, consumer culture, profits, and dreams. If you’re a Carruth fan or up for something a bit offbeat, I think is worth your 15 minutes.

Rehabilitating the economist

Following up on my post Methodology, Ideology from a few days ago, I’ve started to dig in to Johanna Bockman’s Markets in the Name of Socialism: The Left-Wing Origins of Neoliberalism. It is a fascinating perspective on the history of economic thought and the sociology of economics. Importantly, it is explicitly concerned with separating the standard methodology of neoclassical economics from right-wing, capitalist ideology.

I have suffered from an unshakeable paranoia about being an economist ever since it looked like I was going to become one. To be an economist is, as I have written about a lot before, to be generally understood as someone concerned with finance, business, and money, a soulless being who sees human beings as automatons programmed to maximize their wealth. I began to feel—I still can’t shake the feeling—that we are forever condemned to this tragic, villainous role.

Continue reading

More on higher ed funding

Following up on my post from yesterday about higher education funding, I’d like to discuss this article from William G. Bowen and Michael S. McPherson from last week at Vox. I think it is quite representative of the wonky, centrist view—dare I say consensus—that casts the student pays model as a self-evidently “right” approach.

There are many illuminating points in the article. In particular I am quite receptive to their “proposals for reform”: briefly, work to improve graduation rates, reform PhD programs to reduce the oversupply of PhDs relative to academic jobs, professionalize teaching faculty to address the outrageous reliance on mistreated adjunct faculty, and consolidate some small colleges to avoid costly duplication of administrative spending. I think these are excellent starting points for a healthy debate.

But nevertheless I would like to strongly object to the characterization of the funding debate that runs through the first half of the article. I’ll pull a few excerpts that I believe get it wrong on the student pays versus society pays debate.

Continue reading

Who should pay for higher education?


Details might change, but the really big question in higher education funding is always the same: public funding versus private funding. I’m not breaking any new ground here and I’m certainly not advocating anything radical, but it’s on my mind today with “debt-free college” very much in the discussion on the first day of the Democratic National Convention. Every so often I like to refresh my memory on the fundamentals and reaffirm why, on balance, I favor the availability of ambitious, quality, zero-tuition higher education.

Continue reading

Methodology, ideology

From Tim Barker’s review of Johanna Bockman’s Markets in the Name of Socialism:
The Left-Wing Origins of Neoliberalism
, which is currently waiting in my to-read line:

Her real focus is the relationship between socialist politics and neoclassical economics. As her intellectual and political history deftly illustrates, there is no inherent affinity between neoclassical theory, market institutions, and capitalism. (Here she offers a corrective to Marxists like Harvey, whose key text on neoliberalism conflates it with neoclassical economics.) The pioneers of neoclassical economics recognized the relevance of socialism to their project and assumed that one scientific vocabulary could therefore apply to socialism and capitalism.

The conflation of an ideology with the pervasive methodology of economic theory is a disheartening one. It bleeds into the quandaries of teaching introductory economics, into the otherwise valuable methodological critiques and innovations within economics, the characterization of economists as evil.

I submit that (i) we have two words that are slippery to define and both start with “neo-“, and (ii) “economics” is sometimes taken to connote “business” and soulless bean-counting, and so we are stuck with a misconception that I very much wish we could shake.

This conflation is not acceptable to me and I don’t see any easy way to battle it. I do think it argues in favor of an unapologetically wonky Econ 101 that explicitly includes more fundamental methodology, whatever the cost. We must teach our methodology properly if we want it to be interpreted properly.

Coalition building with the disenfranchised

I’ve been thinking about all of the groups that will be affected by the U.S. elections this fall. The basic unit of account for these elections is the vote. Yet so many groups of people that care about the outcome can never be counted in that way.

Citizens under the age of 18; permanent and temporary resident aliens; potential visitors and immigrants; felons; citizens of trading partners, allies, enemies; unborn future generations!

It must be very tough to build a voting coalition of the franchised to win an election. What on earth are we supposed to make of the real or hypothetical interests of disenfranchised stakeholders? Surely the answer can’t just be that the disenfranchisement can be taken as irrelevance—tough luck and out of vote, out of mind?

We have come to expect that coalition-building will favor the interests of older, richer citizens, since they vote in greater numbers (notwithstanding the chicken and egg problem we have there). The young and the structurally disenfranchised are already behind the eight ball, then, before we even open the other cans of worms, the inescapably voiceless.

And yet we do see, sometimes and someways, electoral coalitions that consider some interests of disenfranchised stakeholders. I find that amazing. I can’t help but root for a platform that includes concern for the interests of the ultimate powerless, those without even a vote to throw into the wind. It’s an expression of something beautiful and unlikely.

The most basic one, I suppose, is the old “won’t somebody please think of the children”, and sure, it’s a bit parochial and an easy thing to make fun of, but there might be some method to the madness.

Hold up. One of the knottiest questions I remember from my salad days learning about environmental economics is: when you’re thinking about how to make use of natural resources, how much weight should you put on the interests of future generations?

No matter which way you turn there are traps. Maybe you say “the same or more weight as today’s generation”. So you’re committing to either zero use of resources today, because there are infinite future generations who need to use them. Unless you assume unbounded technological innovation that will let you perpetually squeeze more and more out of less and less. Or you assume that at some future point there will be no future generations. OK, so you say “less weight than today’s generation”. You monster! But how much less weight? Where do you draw the line?

Stupid tradeoffs, ruining everything since forever.

And that’s just “think of the children”! It’s supposed to be the easy one to sell! So, I mean, where do you begin to square these circles in any meaningful way? How many stakeholders can you bring into the tent before it bursts at the seams? It’s not just The Children. The stakeholders spill out everywhere in time and space. Forgotten communities, immigrants, refugees, impoverished laborers in other countries…

Any social system is bound to have stakeholders that don’t have a formal voice. On one reading this is just a supersized version of an externality problem, path-dependent branches winding across time and space to vanishing points we can’t even conceive of. Externalities are quite straightforward in theory: if a private decision has social effects, maybe find a way to have the decision-maker experience some reflection of the social effects.

But what hope is there when the repercussions affect so inconceivably many?

I think the least we can do, then, is to cultivate an empathetic, other-regarding conception of the Public to arm us in our political thinking. I don’t think this is just pie-in-the-sky wishcasting; it’s something that we can learn and practice. It’s one of the roles of humanistic education. We cannot accept the primacy of the insidious marketability criterion for higher education priorities. Humanities, histories of thought, and classics are necessities, not luxuries if we have any hope of sustaining societies that can reconcile stability with diversity of culture or belief.

I’m reminded of George Saunders talking with Trump supporters, from his recent article:

Sometimes I’d mention a Central American family I met in Texas, while reporting another story. In that case, the father and son were documented but the mother and daughters weren’t. Would you, I’d ask, split that family up? Send those girls to a country in which they’d never spent a single day? Well, my Trump-supporting friend might answer, it was complicated, wasn’t it? Were they good people? Yes, I’d say. The father, in spare moments between his three jobs, built a four-bedroom house out of cinder blocks he acquired two or three at a time from Home Depot, working sometimes late into the night. The Trump supporter might, at this point, fall silent, and so might I.

In the face of specificity, my interviewees began trying, really trying, to think of what would be fairest and most humane for this real person we had imaginatively conjured up. It wasn’t that we suddenly agreed, but the tone changed. We popped briefly out of zinger mode and began to have some faith in one another, a shared confidence that if we talked long enough, respectfully enough, a solution could be found that might satisfy our respective best notions of who we were.

Well, let’s not get too dreamy about it.

Yes, let’s not pretend to have solved the world, but it’s not nothing. How painful it can be to internalize the voiceless, but how calming and empowering, too.

This is why I feel wounded by nativist and racial politics. It’s not just the awful content. Its method is not to internalize the voiceless but to demonize them. It equates powerlessness with worthlessness. The coalition is no bigger than the number of votes it can muster: what you see is all you get. The tents get smaller and smaller, a snowballing Balkanization of forgetting, fear, and hostility.

I feel the failure of education. I feel the fragility of the whole edifice of social knowledge. It needs constant work, and if it’s not passed down, it’s gone. And so back to work we go, rebuilding our ability to hear each other over and over again.

Trump does not understand trade (duh)

I can’t believe I’m doing this, and yeah stop the presses, Trump is ignorant about something. But something stood out to me from today’s NYT transcript of David E. Sanger and Maggie Haberman’s… conversation with the Republican presidential nominee.

The headlines were rightly grabbed by Trump’s apparent willingness to violate the U.S.A.’s treaty obligations to the Baltic states. But what stood out to me were his silly statements on trade deficits. What bothered me is less that he characterizes a “trade deficit” as a self-evidently Bad Thing, which he does and I wish he wouldn’t, but that the NYT’s correspondents went along with the characterization.

They challenged him, yes, but kept the implication that trade deficits are indeed bad. Their pushback was that trade deficits are somehow the price the U.S.A. pays for keeping peace around the world? I don’t quite get that. So while I appreciate that we are probably not going to change the general public perception that trade deficits are a Bad Thing any time soon, I think it’s important that we at least try to expose Trump’s policy charlatanism as clearly as we can.

Anyway, here’s what that person who will contest the U.S. presidential election(!) said.

We have massive trade deficits. I could see that, if instead of having a trade deficit worldwide of $800 billion, we had a trade positive of $100 billion, $200 billion, $800 billion.

OK, so first of all, the opposite of a trade deficit is a trade surplus, not a trade positive. That is some high grade Orwellian doubleplusungood nonsense. So bravo I guess for some rhetorical sleight of hand to quickly imply that deficits are simply the opposite of something that is defined as good.

We’re spending money, and if you’re talking about trade, we’re losing a tremendous amount of money, according to many stats, $800 billion a year on trade. So we are spending a fortune on military in order to lose $800 billion.

This is hot garbage. “Lose”? These are the words of a person who has no idea how any of this works. A trade deficits means more imports than exports. Imports are stuff. I love stuff! A country does not “win” if it exports more than it imports. The use of the words “lose” and “win” don’t even make any sense here.

Milton Friedman said this in 1978:

The gain from foreign trade is what we import. What we export is the cost of getting those imports. And the proper objective for a nation, as Adam Smith put it, is to arrange things so we get as large a volume of imports as possible for as small a volume of exports as possible.

We need foreign currency to buy foreign stuff. Foreigners need dollars to buy U.S. exports. So all else being equal one may expect a trade deficit to mean a weaker U.S. dollar. But the U.S. is in a nice, privileged position, in that the U.S. is considered a stable and attractive destination for foreign investment, for example in U.S. Treasury Bills, and investment in U.S. firms. So there is a big demand for dollars in that way, and so the dollar doesn’t get weakened that much. The U.S. gets to have its cake and eat it too. Cool!

This, incidentally, is a factor that also works to keep borrowing costs low for the U.S. government. It is worth noting that earlier in this chaotic Trump campaign, the candidate implied that he would be quite willing to default on U.S. debt. That is one way in which this nice story I’ve just told about the U.S. getting a bunch of cool imports and being attractive to foreign investors could be undermined by ignorant policy. The attractiveness of the U.S. to foreign investors is a crucial part of the story.

For some further reading, here is another simplified explanation of why trade deficits are more Just A Thing than an Inherently Bad Thing.

My reading of this issue with this candidate, and maybe I’m wrong but this is my best guess, is that at least in this case he’s not engaging in the typical misleading or oversimplifying, but genuinely does not have the first idea how macroeconomic policy works. I think he genuinely believes that the trade balance of a country is equivalent to the balance sheet of a firm. That exports are equivalent to expenses and imports are equivalent to receipts.

Not only is Trump, as Ken Burns argues, perhaps the least qualified person ever to be a major party nominee for U.S. President, even those ways in which he is purported to be qualified—his alleged business acumen—are somewhere between nonexistent and actively harmful.