Avinash Dixit is Professor of Economics Emeritus at Princeton University, as well as a Research Fellow at Oxford University. He was President of the Econometric Society in 2001 and President of the American Economic Association in 2008. He’s been elected to both the American Academy of Arts and Sciences and the National Academy of Sciences.
Beyond being credited for the Dixit-Stiglitz model of monopolistic competition, which underpins much of modern trade theory, Mr. Dixit is renowned for his work in game theory, microeconomic theory, international trade, and development. He’s the author of eleven books, including Investment Under Uncertainty, Thinking Strategically, and The Art of Strategy: A Game Theorist’s Guide to Success in Business & Life.
The Politic: Starting off with the basics– what’s game theory, and how does it relate to the concepts of punishment, threats, and crime?
Avinash Dixit: Game theory, as you know, is the analysis of strategic interactions, and they can arise in all kinds of contexts: negotiation, cooperation, contracts, and mixtures of those. Things like punishments, threats, and so on, are particular kinds of strategies that may help in some of those situations.
Could you give an overview of your theory of ‘graduated punishment?’ As I understand it, the idea is that – in theory – there’s some optimal punishment size for a crime which balances deterrence with over-penalization, and we should start with small punishments and gradually work upwards– how’s that sound?
Actually, very oddly, formal game theory to my mind gets this wrong, although it’s understandable how they get this wrong. The usual idea, especially in the context you’re asking about – prisoners’ dilemmas – is to start with the maximal credible punishment right at the beginning, because the idea is that that will be the most severe threat and so will illicit the best cooperation. But in reality, everybody who’s looked at the way punishments are designed finds that the successful ones are done in a graduated way. You maybe start with just telling somebody, “hey you’re not behaving the way I want to ensure.” If they persist, then you go to the next level of giving them some kind of a warning, and then start with a minor punishment.
If you think about it, there are very good reasons for doing that: it might just be a mistake the first time or they may be trying something to see how far they can get away with it, and you want to gradually make them aware that they’re not going to do so. Especially Elinor Ostrom, who did a whole lot of research on cooperation in collective action and common resource pool problems, found this time after time– that just hitting the maximal punishment right at the beginning is not a good idea. If it’s been a mistake or something like that, why endanger a good, longer-term relationship immediately?
So if we take the example of climate change, for instance, it sounds like you wouldn’t want to start with the maximal credible punishment; instead you would gradually increase the penalty. But might it be true that – in the real world – we’ve started too light, and that people have become conditioned not to take personal responsibility for their actions as a result? Is it possible that graduated punishments can become infeasible?
Climate change is a particularly difficult example– partly because its costs, and in some cases its benefits, are very unequally distributed over the world. There are countries that might actually benefit from climate change like parts of Canada and Russia. Then, of course, there are people, and maybe countries, that don’t really believe climate change is real at all, so it will be difficult get them to take any kind of costly action. That’s one case where I actually don’t really know what a good solution would be. We will probably never persuade, at least in the immediate future, the U.S. to play along. People thought that China would never play along, but it’s slowly coming along to recognize that it’s a real problem, and that they should contribute to solving it.
But that’s an extremely difficult one, partly because so many parties are involved, and as I said, the costs and benefits are so unequally distributed. Remember, Ostrom found conditions for successful resolution of collective action problems, some of which are that the stakeholders should be well-defined, free-riding by outsiders should be difficult, and the assignment of duties should be reasonably clear. That’s why, for example, she found that lake fisheries are reasonably able to come to agreements on restricting over-fishing, but ocean fisheries find that very difficult.
Unfortunately, formal modelling of graduated punishments is extremely difficult. I’ve tried that myself in collaboration with a couple of game theorists who are much more powerful in the theoretical apparatus than I am, and we didn’t really get anything very satisfactory. It’s really – in my mind – one of those unresolved research problems.
What do you see as the biggest problems in formal modeling?
There are several that are hard-to-describe. In technical terms, formal models have got to have a combination of moral hazard and adverse selection: you’ve got to have good types and bad types, you need experimentation to find out whether the person you’re dealing with is really a bad type or is a good type who just made a mistake, and you’ve got to have the possibility that someone who’s not really a bad type might just try and see how much they can get away with. It’s simply the math of that that gets quite tricky.
You highlight that many game theorists prefer using “abstract mathematical facts” but that you and your co-author see it as necessary to factor in “social and psychological aspects of the game.” Given the difficulties in modeling these complex relationships, do you think the strength of game theory is in finding solutions, or in formalizing general guidelines? How do you work through that?
It’s a combination– you’ve got to go back and forth. What we’re saying is that the solution to a game often is not realistically found by, say, labelling the players “row” and “column” and the strategies “1, 2, 3, 4.” But if you put into the definition the composition of the game, the kind of cultural-historical context, then you’re much more likely to get a realistic solution.
The best example of that might be in a different context– coordination games. Think of two players who have to each choose one of two colors. They’re in separate rooms. If they choose the same color, they’ll both get a prize. If they choose different colors, neither will get a prize. In this case, their interests are perfectly aligned: they want each one to choose the color that the other chooses. But which one? It greatly helps to have a common understanding.
Suppose the colors are blue and orange. Two Princeton students will choose orange. Two Yale students will choose blue. If one is Yale and the other is Princeton, it gets tricky. The ability to coordinate on both sides comes not from anything abstract in the game, but cultural understandings of where they come from and what’s common to them.
That reminds me of your example where people travel from New Haven and Boston to New York, trying to find each other, and intuitively converge on the clock at Grand Central Station.
That’s Schelling’s classic example. The focal point used to be below the clock at Grand Central Station at 12:00pm, noon. But the other thing is that cultural understandings change. These days, of course, some of that becomes irrelevant because people have cellphones. You can call and say, “hey, where are you going?” If you take that away, I don’t know that people would still meet at Grand Central Station. That’s what we mean by the ‘context’ in which the game is played, and who’s playing it, are often very important in trying to understand or predict the outcome.
So there’s the problem of cultural difference when you’re trying to predict outcomes. I imagine you could have a case where there are a million different variables – a million different preferences – and that would be difficult to model. But what about a case where you simplify to two variables?
For instance, some people might be in favor of drug criminalization because it reduces crime, while others might be opposed to it because it disproportionately hurts minorities and reduces equality. Even with just two variables, how would you make tradeoffs between these fundamentally different values?
In the ultimate limiting case of what you’re saying, which is a zero-sum game, when one person gains the other necessarily loses. It’s going to be very difficult to come to a successful negotiation outcome– unless there’s something else that both sides don’t want to happen. Let’s suppose you tell these people who are negotiating over whether to be lenient and treat drug use as a medical problem, or to be tough and treat it as a criminal problem, that unless they come to an agreement, there will be a nuclear explosion and the whole world will blow up. Neither will want that to happen, and possibly depending on who is more patient, who is tougher in some way, a solution will favor one or the other. There’s got to be something like that. This, again, is an insight from Schelling: bargaining is not a zero-sum game. Successful negotiations rely on there being some kind of backstop threat point that both of them want to avoid, so their interests are at least aligned in that. Among all the various possible compromises that are better than that threat point for both of them, whether the agreement is more favorable to one or more favorable to the other is the question.
How can you compromise on something that might be as hard to quantify as equality?
Very often what happens it that it’s not just one issue that’s being talked about, but there’s a second issue that’s simultaneously on the table. That, say, might be abortion. Then, compromises become possible because the two parties might not trade-off the one issue against the other at equal rates, so it may be that each gets something closer to its position on the issue that’s relatively more important. That, in a way, is exactly the way in which international trade works.
You know the classic comparative advantage idea– that maybe the best lawyer in town is also the best typist, but his comparative advantage might be in law, so he doesn’t do his own typing but hires a typist. A similar kind of unequal rates of transformation of one thing into the other allows compromise across two issues.
And the third thing that happens, again in the international context, is there being more players. It may be that A has something that B wants but B doesn’t have anything that A wants, so there is no bilateral deal. But there may be a C, such that B has something that C wants and C has something that A wants, so the three of them can reach a deal that benefits them all.
More issues and more persons, in principle, is favorable to successful resolutions of negotiation. Of course, what can happen is that they can also take up unreasonable issues and threaten each other in ways that might compromise the whole interaction.
If we think about Ostrom’s guidelines for collective action again, is it possible that if you have more players, the rules of membership become less clear?
Not automatically or necessarily, but yes, you basically need to set up a system that defines, for example, how new members might be admitted, or whether any one of the existing member can block a new one the way some clubs do. Under certain conditions, you might also prefer that the World Trade Organization, for example, has rules that say: “so long as your economy is abiding by such and such rules, you can join.”
So Ostrom outlines about five rules as you mention. If we take something like international law, one of her rules is that everyone should have information available to them while designing a game’s rules. But when we’re dealing with changing cultures and changing intergenerational trends, how do you make sure everyone has access to the same information, and how do you balance over-specifying rules with maintaining flexibility?
You have to be aware of this– I don’t know if there’s any one formula. Very often the issue with constitutions is that they are intended to deal with not just one issue, but a whole lot of issues, and not just those that are currently on the table, but those that might come along over the course of time.
That’s why there’s actually a whole hierarchy of things. Constitutions should really not lay down things in fine, fine detail. There should be fairly broad principles that will persist through time. You’ll want subsequent generations to hold onto these things, and that’s why they should be hardest to change. Then at the next level will be things like legislation that the next Congress can change or the next Senate can change, which will last for a number of years and have somewhat more detail. Then, final details are filled in by regulators. I’m not saying that what we’ve got is exactly correct, but the general principle – that there should be a hierarchy of relatively broad, general principles that are hardest to change, down to tiny details that can be changed as circumstances change fairly quickly – is the right way to go.
If we relate this back to crime and deterrence, and we’re trying to find an optimal punishment size, does it make sense then that a decentralized authority could allow us to test more points?
That does kind of cross-cut against each other. If you have a very broad, general constitution that you want the whole country and subsequent generations to follow, that’s going to be hard to do in a decentralized way. For a lot of the particular problems that come up, where there’s a lot of local information like in Ostrom’s communities, they’re better handled bottom up than top down. And in fact, people are realizing that bottom-up organization does a lot more than not only centralized planning but also relatively controlled economies like France. But there’s got to be a mixture of things– there’s no kind of one size or one formula that fits all nations and all times.
If we take the example of gun laws for people with mental illnesses, it seems like finding the optimal punishment might be hard because there’s so much deviation and unpredictability in peoples’ utility functions. How do you try to find the point at which they converge given that uncertainty?
If I really knew the answer to that, I’d be out there shouting it out! This is one of these extremely difficult and probably unsolvable issues. If two sides both say, “this is extremely important to me and I’m not going to give an inch on it,” and they’re on opposite sides, maybe there is no compromise.
Let’s switch it up a bit— it was interesting to read about the ‘random’ strategy for prisoners’ dilemmas. Could you briefly outline it?
The best example of that– you’ve probably seen the Princess Bride. Remember the ‘battle of wits’? There’s no systematic resolution to this any more than there’s a systematic which way to decide whether you kick a soccer penalty to the goalie’s left or right. These are the classic circumstances in which randomizing is important because it keeps the other party from taking advantage of something systematic you do: it stops them from exploiting your system.
Do you think the random strategy fits with what we’re seeing from Donald Trump, where he might go back and forth on an issue or is kind of unclear on where he stands?
It could be. There’s the famous Nixon ‘madman theory’ that opponents like Gadhafi would be saying: “we have to be careful dealing with that guy Nixon– you never know what he’ll do!” Schelling actually many years earlier said the line: “if a man knocks at a door and says that he will stab himself on the porch unless given $10, he is more likely to get the $10 if his eyes are bloodshot.” (This is from his book The Strategy of Conflict, p.22.) So that kind of randomization might be a deliberate strategy. But again, there might be something else: it may be that people selectively hear what they want to hear, and that confirms their biases, or their hopes. So saying different things at different times may be trying to exploit that bias, such that Trump’s base will hear what he’s saying one way, and the opponents will hear something else and think: “Oh, maybe he’s going to be sensible this time after all.” That could be a good strategy.
Let’s imagine that somebody is playing the random strategy, and they’re playing it on a global strange where they’re affecting a lot of actors. How does that relate to the idea of credibility, and how does that factor into the short-run vs. long-run?
Actually, in a way, leaving things uncertain can make some threats credible. It’s going to be very difficult in a nuclear confrontation for one side to say, “do such and such, and I will with 100% certainty blow up the world.” The other side realizes that when it actually comes to blowing up the world, you will flinch. But you can credibly say, “hey, risks are rising– keep doing this and things may get out of control.” Or to give you a simple, homely example: a mother cannot credibly say to a child, “do such and such, and I will beat the daylights out of you.” But she can credibly say, “do you want mommy to get angry?” The child knows that mommy, in her anger, may do things that she might not rationally want to do, and that can be a useful deterrent threat. Again, everything goes back to Schelling. This is Schelling’s idea of ‘brinksmanship.’
If mommy says, “don’t do that or mommy will be upset,” in the short-run, that might be a good strategy: it keeps you on your feet and you might want to comply. But in the long-run, what if she doesn’t follow through? Occasionally, you have to carry things out. If the child starts testing you, and then mommy always, always back down, then the child will eventually think this is an empty threat. Maybe wrongly so, but the child will ultimately come to think like that. In an actual instance, the Fed might say, “we won’t bail out all banks that are in trouble because otherwise banks will behave recklessly, and they’ll know they’ll get bailed out.” Occasionally, the Fed has to let somebody go, and maybe rightly or wrongly as things turn out. Lehman brothers was that kind of example.