An obvious caveat: My observations are biased due to the fact that I’ve only seen parts of America (California, part of the Northwest, part of the Midwest, and New England), and only parts of Europe (Central Europe, part of Scandinavia, part of France and England). One should realize that large cultural, political and economic differences exist both within the US and Europe, so all the statements below refer to averages with wide confidence bands around them.

Economic life:

- Prices are normally stated net of sales taxes. (high confidence, uncontroversial)
- Tips are higher and more common. (high confidence, uncontroversial)
- Tap water is much more heavily chlorinated. (high confidence, uncontroversial)
- Air-conditioning is vastly more common both in private homes and offices. (high confidence, uncontroversial)
- The average quality of houses is much lower. (high confidence, somewhat controversial)
- The proportion of people living in single-family houses as opposed to apartment buildings is much higher. (medium confidence, uncontroversial)
- The price of gasoline is about 50% lower. (high confidence, uncontroversial)
- There are both more cars per person and cars are much bigger on average. (medium confidence, uncontroversial)
- Automatic cars are vastly more common. (high confidence, uncontroversial)
- The price of necessities (food, clothing, personal hygiene) is lower, but not much, and the quality is generally lower. (low confidence, highly controversial)
- Food is bought and sold in much larger quantities. For instance, the smallest available bottle size for milk is usually half a gallon (about 1.9 liters). (high confidence, uncontroversial)
- Extreme obesity is vastly more common. (high confidence, uncontroversial)
- The quality of infrastructure (roads, railways, electricity grid) is lower. (medium confidence, somewhat controversial)
- Roads are more often built in strictly rectangular patterns, both in cities and on the countryside. (high confidence, uncontroversial)

Social life:

- Racial diversity is immensely higher, especially in urban areas, but also in rural areas. (high confidence, uncontroversial)
- So is religious diversity. (high confidence, uncontroversial)
- Religion plays a more central part of public life, including in politics (high confidence, uncontroversial)
- Interest in family history and genealogy is much higher. (high confidence, uncontroversial)
- Bodily contact between people in everyday interactions is much less frequent and more often regarded as inappropriate. (medium confidence, somewhat controversial)
- Conversations are much less formal both in professional and private contexts. (medium confidence, uncontroversial)
- Small talk is a much more important part of everyday life both in professional and private contexts. (high confidence, uncontroversial)
- Adolescents and young adults seem to be more mature both in terms of physical appearance and character development. (low confidence, highly controversial)
- Elderly people seem to be more familiar with, and more adept at, using new technology as well as social media. (high confidence, somewhat controversial)
- Knowledge about foreign countries (geography, history, politics) is generally much poorer. (high confidence, highly controversial)
- Patriotism is more wide-spread, more frequently expressed and more strongly felt. (high confidence, somewhat controversial)

Political life:

- There are more elected (as opposed to appointed) public officials and elections occur at higher frequencies. (high confidence, uncontroversial)
- Personal political opinions are more frequently expressed in public. For instance, pumper stickers with political messages are a much more common sight. (medium confidence, somewhat controversial)
- Political polarization is more profound. (medium confidence, somewhat controversial)
- There are more prohibition and warning signs on the streets as well as in public and private buildings and facilities. (low confidence, highly controversial)
- There are more local political initiatives such as petitions, awareness campaigns, fund raising events etc. (medium confidence, somewhat controversial)

Goffman on page 6 then states the following: “Take, for example, techniques that pedestrians employ in order to avoid bumping into one another. These seem of little significance. However, there are an appreciable number of such devices; they are constantly in use and they cast a pattern on street behavior. Street traffic would be a shambles without them.”

In this post I want to take up this claim and provide a model that allows us to discuss how people avoid bumping into each other. I will use Goffman’s work to help me to identify the appropriate model for this issue.

Let me first identify the players. It seems that, while there are many people involved in street traffic, typically we encounter these people one by one. So I think for a first attempt it might be sufficient to study the situation of two people who are currently on course to bump into each other and who are trying to get past each other in order to avoid a collision. So we have two **players** in often fairly symmetric positions. Now here is one statement by Goffman (on page 8) about **actions**: “Pedestrians can twist, duck, bend, and turn sharply, and therefore, unlike motorists, can safely count on being able to extricate themselves in the last few milliseconds before impending impact.” Despite the fact that Goffman mentions so many possible actions I will for a first attempt consider only two. Try to pass on the left or try to pass on the right. But if we feel it may be useful we can go back and think more about the possible moves pedestrians can make. Now what about **payoffs**? Talking about cars or road traffic, Goffman, on page 8, states that “On the road, the overriding purpose is to get from one point to another.” For pedestrian or street traffic he states “On walks and in semi-public places such as stadiums and stores, getting from one point to another is not the only purpose and often not the main one”. He has more to say about payoffs on page 8: “Should pedestrians actually collide, damage is not likely to be significant, whereas between motorists collision is unlikely (given current costs of repair) to be insignificant.” All this strikes me as important to understand pedestrian traffic. Let me see why. Suppose we ignore these last few statements, especially the one about pedestrians often having more than one purpose. We might then be tempted to say, and perhaps this is a good model of car traffic, that the game is simple. We have two players (the drivers facing each other), each has two possible choices (pass on the left **L** or pass on the right **R**) and if they pass each other that’s great (they both get a payoff of say **one**) and if they bump into each other that’s awful (they both get a payoff of say **zero**). In other words the game can be written in matrix form as follows:

What are the evolutionary stable norms of behavior in this game? They must be a Nash equilibrium, which means no player should have an incentive to deviate from the norm. Could the norm be that everyone passes on the right? Yes! If everyone passes on the right, you would be foolish to pass on the left, because that would mean you bump into everyone and get a payoff of zero! If you instead also pass everyone on the right, you indeed do get past everyone and you enjoy your payoff of one. Completely analogously the norm could be that everyone passes everyone on the left. And indeed both of these norms exist for car traffic. In Japan people drive on the left, in Chile they drive on the right (most of the time). Recall that Goffman was well aware of the possibility of different norms being possible (in different societies or places) – see the previous post.

A quick aside: game theory experts will have noted that the game has a third Nash equilibrium, an equilibrium in so-called mixed strategies. Under a Harsanyi purification (Harsanyi, 1973) interpretation of this mixed equilibrium we could describe it like this. Half of all people pass on the left and the other half of all people pass on the right. This is an equilibrium, because if that’s indeed what the others are doing you are equally well of passing on the left and passing on the right: half of the time you avoid an accident and the other half of the time you are dead (have an accident) either way. This is an equilibrium, but not an evolutionary stable one. Why not? Suppose slightly more than half of all people pass on the left. After a while you might notice this and then you find it slightly better to also start passing people on the left. But then the more people pass on the left the better this strategy becomes and gradually we move towards the norm of everyone passing on the left. This is probably more or less how the whole thing evolved in the early days of cart traffic. You may want to read Peyton Young’s “Individual Strategy and Social Structure” Princeton University Press (2001).

This all seems fine for cars, but what about pedestrians who supposedly, according to Goffman, use many “devices” and “techniques […] in order to avoid bumping into one another”? There seems to be absolutely no need for this here. So I think something is missing from this game. We should recall that pedestrians, according to Goffman, have side interests in addition to getting from A to B as fast as possible. It does not seem to be the pedestrian’s only goal to get past the oncoming person, the pedestrian might have a slight preference for which side would be better for her. Think of a person that you face in a corridor and that person, after they pass you, would like to turn left to the bathroom for instance. This person probably has a slight preference, when possible, to pass you on her left. The problem with this now is that you don’t necessarily know that she wants to go to the bathroom, and thus, you don’t know that she prefers passing you on her left. That’s why she might want to use a “device” – a signal of some sort – that tells you that she wants to pass on the left. Ok, so hold on a moment. We need to proceed slowly. I first need to discuss this game without “devices” so that we can see why “devices” might be useful. So how do I take into account these possible side issue preferences that pedestrians might have? Well, I need to modify the payoffs people get and these payoffs are now different for different people and I need to make the information about these preferences private. What I mean is that I will assume that everyone knows their own preferences (or payoffs) – they know whether or not they want to go to the bathroom on the left after they pass you – but you, their “opponent” do not know. So how does this work? I will simply change the game as follows:

What are these u’s and v’s? You should think of each u and v representing a possible person with a particular preference for passing left and right. A person with a u (or v) close to a half is a person who cares only about getting past their “opponent” and does not care in any way on which side this happens. A person with a u (or v) less than but close to one is a person who would much prefer to pass their “opponent” on the right. Say this person really urgently needs the bathroom just behind you on her right. A person with a u (or v) greater than but close to zero is similar but has a strong preference to pass on the left.

How do we do this? Well, this is one of Harsanyi’s great contributions to the body of game theory. We assume that both u and v are drawn from some distribution F on a subset of the real line that includes the interval from zero to one. Then every person learns their own u (or v) but learns nothing (as yet) about their opponent’s v (or u). Every person only knows that her opponent’s v (or u) is random and that the randomness is described by the cumulative distribution function F. In fact we here make a radical assumption and one that we should probably challenge later. We assume that not only does every person believe her opponent’s v (or u) is distributed according to F, but we also assume that everyone knows this fact, and that everyone knows that everyone knows this, and so on ad infinitum (as game theorists like to say). In short we assume that this distribution F that governs the likelihood of the various preference types you might encounter is **common knowledge** among the two players. Modern game theory also has ways of dealing with deviating from this assumption. But for the moment we shall assume it. Under an evolutionary interpretation this assumption is less worrisome than one might initially think, but we should probably come back to it.

So how do we “solve” this game? There are two ways one can look at a game with incomplete information. One can either consider each possible person (with a specific u or v) separately – the so-called interim view – or one can consider the problem from the ex-ante point of view, where each person has a strategy for all possible u’s that this person could end up with. These two approaches are equivalent but sometimes one is easier than the other for the analyst. Here the second, the ex-ante, approach is easier. So consider a person who many times throughout her life has to navigate pedestrian traffic. In each situation she might have a different u. Sometimes she just wants to get past her opponent, her u is a half, sometimes she wants to turn left right after passing her opponent, her u is close to zero, sometimes she wants to turn right right after passing her opponent, her u is close to one. She develops a strategy as a function of her u. Now what would be a good strategy? Suppose there is some norm of behavior that people follow, a function from their u’s to passing left or right. For some such norm, what would be the best individual response to this norm? As you with your u do not know your opponent type, their v, knowing the norm that is in place only tells you with what probability (or frequency) your opponents will choose left or right. Suppose you know this probability of opponents going left (from your knowledge of the norm and the distribution function F) and call this probability , then what is your implicit tradeoff between going left and going right? Recall that we are at the moment studying a situation where people do not communicate with each other (they do not use any “devices”). Well, if you go left you avoid bumping into each other with probability and you do bump into each other with the remaining probability . Your average (or expected) payoff from going left yourself is, thus, . Similarly, your average (or expected) payoff from going right is . When is left (strictly) better than right for you? Well if and only if . Calculating we get .

This means that, whatever the norm is, your best response to this norm is to use a simple cut-off strategy. Basically what you do is this. You observe the frequency of people going left and right (induced, as we said, by the combination of the prevailing norm and the distribution of preference types F) and you choose left yourself if your u for this interaction is less than the observed frequency of left and choose right otherwise.

But if this is your best response to this norm, then it is everybody’s best response to this norm and it will become the norm itself! So everyone will be using the same cut-off strategy! But what will the cut-off be? Well if everyone uses a cut-off of say x, some real number between zero and one, then the probability that people use action left is the probability that their u is less than x, which is given by . So if the cut-off people use is x, the probability of people going left is F(x) and this is the best response cut-off they will use. So we must have that x=F(x).

So any stable norm must at least satisfy that we are in equilibrium, meaning that x=F(x). But is this enough for a stable norm of behavior? Not quite. To discuss this it is best to consider two examples of possible distributions F that could be present in different places of human pedestrian traffic.

Suppose the preference u is, like so many things in life, normally distributed. Let’s say it is normally distributed with a mean of a half and a relatively low variance so that not too many people have a u less than zero or more than one. Please excuse the low tech (but I think sufficient) rendering of this example:

What are the Nash equilibria of this game with such a distribution F? There are three. First we have F(x)=x for a value of x that is positive but pretty close to zero. What does this mean? It means that the norm is such that almost everyone attempts to pass others on the right except for very few people who have a very strong interest to pass on the left. This is an equilibrium that is pretty close to the equilibrium of the car-driving game of always driving on the right. There is a similar equilibrium with x=F(x) where x is just less than but very close to one. Here almost everyone attempts to pass others on the left except for very few people who have a strong interest to pass on the right. There is another equilibrium, however, at x equal to one half, where we also have x=F(x). Here we have that everyone who has the slightest inclination for passing on the left attempts to pass on the left and everyone who has the slightest inclination for passing on the right attempts to pass on the right. This is a mayhem equilibrium. But is it stable? No. Why not? Suppose that people use a slightly larger cut-off than one half, call it y. Then we find that, as F is quite steep at one half, F(y) > y. This means that no people’s best response cut-off F(y) is higher than the prevailing cut-off of y. So we expect people to adjust their cut-off upwards. This will go on until we reach the other equilibrium with a cut-off close to one. Similarly, a cut-off of just less than one half will lead to lower and lower cut-offs and eventually to the equilibrium cut-off close to zero.

So what have we achieved? Not so much. The whole situation is very similar to the much simpler game without the u’s and v’s and all that. So, again, it seems that we would not need any “devices” and “techniques” of “scanning” and “intention display” (Relations in Public, pages 11 and 12) in this situation. Even without this we obtain a stable norm of behavior in which there are (almost) no collisions. I will come back to this after another example.

Suppose now that the place of pedestrian traffic that we are interested in has a very different F. Suppose that most people have a relatively strong preference for either left or right. For instance you can imagine a doorway that people need to get through before they then want to turn left or right pretty quickly after that. For these people, encountering each other in the doorway, the density f behind the cumulative distribution F is probably best described as being relatively high around low and high values of u and relatively low for medium values of u close to one half. Let us assume that F is symmetric around one half. Let us also assume that still there is almost no weight (in f) on values of u less than zero and larger than one. A picture of this situation:

Now what equilibria do we get here? Actually we get only one equilibrium and it is a mayhem equilibrium. It is cutoff equilibrium with cutoff x equal to one half, much as the mayhem equilibrium in the normal distribution case. But now the mayhem equilibrium is stable. Why? Because F is rather flat around the value of one half, if we consider a cut-off of y that is slightly larger than one half we have that F(y) < y and the best response cut-off is thus smaller than the y cut-off and we expect that the cut-off evolves back to a value of one half.

By the way, what I have described here is essentially the paper “Evolution in Bayesian Games II: Stability of Purified Equilibrium” by Bill Sandholm, Journal of Economic Theory, 136 (2007), 641-667.

Now you might say that we do not often observe such a stable mayhem equilibrium and you are probably right. In fact this is where we should finally introduce Goffman’s “devices” and “techniques” of “scanning” and “intention display” (Relations in Public, pages 11 and 12). The way I would model this (and this is now finally ongoing research I am currently undertaking with Yuval Heller at Bar Ilan University) is as follows. I would allow the players after they know their own u to send one from a set of possible messages to their opponent, to be understood as their “intention display”. I would assume both players are “scanning” for messages of their opponent and that the players can then condition where they try to pass their opponent on the two observed messages. You may want to think about this as players making a slight movement towards the left or right (this can be done a long time before the two actually meet) with the idea of signaling their intention as to where they would prefer to pass their opponent. What Yuval and I find so far is that for many distributions F (including the two I mentioned before) there is a universal and simple strategy (or norm) that is evolutionary stable. If you have a u less than one half you send the message to be read as “I intend to pass on the left” and if you have a u greater than one half you send the message to be read as “I intend to pass on the right”. If both send the same message they follow through with their displayed intentions. If they send different messages – that is, a slight conflict of interest is revealed – they fall back on a background norm of always passing on the left (or always passing on the right). We are not quite done yet with this project, but I hope you will be able to read about it very soon.

So how did game theory add to Goffman’s study? In many ways I think. First, we had to be very explicit about the various strategies (potential norms) people could be following in our model. Second, we can then explain why a specific norm among all the potential norms is expected (a stable equilibrium). Third, the formal analysis allows us to identify conditions under which different potential norms are stable or unstable. Fourth, we can now ask new questions. For instance, is a stable norm of behavior in pedestrian traffic efficient (maximizes the sum of utilities)? The answer, by the way, is typically no. And finally, the theory is so explicit in its predictions that it can be tested.

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The books we used were “Behavior in Public Places – Notes on the Social Organization of Gatherings” published by The Free Press (1966), from which students decided to read Chapter 6 “Face Engagements” and Chapter 9 “Communication Boundaries”, as well as “Relations in Public – Microstudies of the Public Order” published by Basic Books (1971), from which we discussed the preface as well as parts of Chapters 1 “The Individual as a Unit” and 2 “Territories of the Self”.

In this first of at least seven posts that I have planned on this subject, I explain why Goffman’s work is very amenable to game theoretic analyses and what game theory could possibly add to Goffman’s work.

Goffman’s is, in his own words, a “naturalistic” study of the “public order”. He identifies the often subtle norms of behavior that underlie everyday human interaction and provides insights into why these norms are as they are.

So why is this suitable for a game theoretic analysis? The everyday human interactions that Goffman describes and discusses are often between a small and well-defined group of individuals. These are the **players** in the game. In fact often it is about two individuals only. It is often relatively straightforward to see what possible **actions** people can take and Goffman describes the possibilities very well. In fact he employs, among other things, an extremely clever method by comparing everyday human behavior in the “normal” sphere with human behavior in a mental hospital. This allows Goffman to see what possible actions people could have chosen, but typically do not choose in the “normal” world. Finally, Goffman identifies the goals that people have in these interactions. This is what a game theorist calls the individual’s **payoffs** or utility. These are here rarely in monetary terms. But this is all we need for a game theoretic analysis: players, actions, and payoffs.

Well, one more thing should be discussed: **information**. Who knows what? In fact in most of the human everyday interaction that Goffman discusses there are bits of information that not everyone who participates in the interaction has. One of Goffman’s other books has the title “The Presentation of Self in Everyday Life”. We would not need to present ourselves in some way or another if our co-players in the interaction know everything about us from the beginning. In fact information, and who knows what, will be important in most of the examples that I will discuss in this series of posts. By the way, Goffman was well aware of the game theory of his time, such as von Neumann and Morgenstern’s 1944 book “Theory of Games and Economic Behavior” including zero-sum games as well as Schelling’s work including that on coordination games, focal points, and conflict. He could hardly have been aware of Harsanyi’s important work on incomplete information game theory as that came in the very late 60’s and early 70’s and most of Goffman’s work predates this. But this theory of incomplete information game theory will be very useful to us in our game theoretic modelling attempts of selections of Goffman’s work.

So I have argued that game theory is highly suitable to study human everyday interaction as Goffman describes it. But game theory is actually not one theory; it is a collection of many theories. In fact it is probably better termed a collection of models and solution concepts. A solution concept, as much a misnomer as the term “game theory” itself, is simply what we expect the outcome of the game to be. Game theory, however, is awash, if this is the term I want, with solution concepts, from the many concepts of dominated strategies and rationalizability (in simultaneous and sequential interaction) to the many possible refinements of Nash equilibrium. And, by the way, I have already implicitly restricted attention to non-cooperative game theory. There is a whole world of additional solution concepts for models of cooperative game theory. I think, however, that for the most part Goffman’s work is best understood using non-cooperative games (as described above) with the solution concept of **evolutionary stability**, typically a particular case of **Nash** **equilibrium**.

This is so because human everyday interaction satisfies all the assumptions of evolutionary game theory. The interaction is relatively small-scale, short-lived, and simple (much simpler than chess, for instance), the interaction is “recurrent” meaning we face the same kind of interaction many times in our life and with often changing “opponents” (not like the interaction we have with our family members or co-workers – which however could also be studied, albeit with somewhat different tools and solution concepts – see e.g. my blog post on lying II and III). This is the setting in which theory finds that we can, in many cases, expect Nash equilibrium play. In fact we can even expect special Nash equilibrium play, equilibrium play that is also evolutionary stable, stable, that is, with respect to small changes in behavior. For an overview of the findings of evolutionary game theory see for instance the books “Evolutionary Game Theory” by Jörgen Weibull, MIT Press (1995), “Evolutionary Games and Population Dynamics”, by Josef Hofbauer and Karl Sigmund, Cambridge University Press (1998), and “Population Games and Evolutionary Dynamics” by Bill Sandholm, MIT Press (2010).

Now, finally, why is Goffman’s work especially amenable to game theoretic analyses? This is because Goffman’s view of these everyday human interactions and the norms that guide them is already very close to those of an (evolutionary) game theorist. For instance, on p.xx of the preface to “Relations in Public” he states that “the rules of an order *are* necessarily such as to preclude the kind of activity that would have disrupted the mutual dealings, making it impractical to continue with them.” Translated into the language of game theory this means that the rules are such that individuals cannot benefit from deviating from them. In other words these rules constitute a Nash equilibrium. On p.xx he states further that “However, it is also the case that the mutual dealings associated with any set of ground rules could probably be sustained with fewer rules or different ones,…”. In other words Goffman recognizes that many games have multiple equilibria. On p.xx he continues the last sentence as follows: “…, that some of the rules which do apply produce more inconvenience than they are worth.” In other words he realizes that Nash equilibria are not necessarily efficient.

Another quote from “Relations in Public” on p. 59 perfectly demonstrates Goffman’s game theoretic view: “Second, the traditional way of thinking about threats to rules focuses on a claimant and a potential offender, and although this certainly has its value, especially when we examine closely all the means available for introducing remedies and corrections, still the role of the situation is usually thereby neglected. A better paradigm in many ways would be to assume a few participants all attempting to avoid outright violation of the rules and all forced to deal with the contingencies introduced by various features of various settings. Here the various aims and desires of the participants are taken as given – as standard and routine – and the active, variable element is seen to be the peculiarities of the current situation.” The participants are the **players**, their various aims and desires are their goals or **payoffs**, and the situation is the collection of the sets of available **actions **(based possibly on whatever **information** players have). Goffman, thus, suggests we can keep players and their goals fixed and consider how the structure of the game, the situation these people are in, induces human behavior. This is very much the view of game theory as well.

To show you that a formal game theoretic analysis can provide additional insights over those gained by Goffman himself, I will, in at least the next six blog posts, actually build game theoretic models based on Goffman’s work (and based on the class discussion the students, Carlos, and I had at CICS). You can then check for yourself whether or not you see added value in these formal models. The “proof of the pudding is in the eating” as they say.

]]>Therefore I decided to set up a small survey consisting of only 3 questions:

- What is economics?
- What is economics good for?
- What is the most important insight economics has to offer?

You can answer these questions in short or long form, anonymously or with your name. I’d like to get as many different perspectives as possible, so I would encourage you to share this post and/or the survey link below on your social media pages. Warning: I may quote your response in a future post and I may steal it if it’s better than mine.

https://freeonlinesurveys.com/s/XtU7oo9d

Looking forward to reading your answers!

]]>Der Klimawandel ist die Mutter aller Externalitätenprobleme. Unsere CO2-Emissionen hier und heute haben einen Effekt auf das globale Klima in der fernen Zukunft – und die Veränderungen im globalen Klima haben wiederum eine Reihe von komplexen, schwer vorhersehbaren und höchst unterschiedlichen Effekten auf Ökosysteme und unsere Gesellschaft.

Österreich hat sich mit den anderen Staaten dieser Welt im Pariser Abkommen dazu verpflichtet CO2-Emissionen zu reduzieren in der Hoffnung damit die globale Erwärmung auf 2 Grad gegenüber dem vorindustriellen Zeitalter zu begrenzen. So weit, so gut, obwohl man an der Effektivität und auch an der Sinnhaftigkeit des Abkommens zweifeln darf. Aber lassen wir diese Debatte beiseite und schauen wir uns lieber die neue „Klimastrategie” der österreichischen Bundesregierung an.

Was steht da drin? Im wesentlichen will die Regierung dass es in Zukunft keine Ölheizungen mehr gibt, dass möglichst viele Gebäude thermisch saniert werden, dass mehr mit Bahn und Rad und weniger mit Autos gefahren wird und wenn, dann mit Elektroautos.

An der Strategie wurde in den letzten Tagen viel kritisiert. Zu wenig konkret sei sie, die Finanzierung der vorgeschlagenen Maßnahmen sei unklar, die Zuständigkeiten seien nicht geregelt, usw.

In meinen Augen ist diese Kritik völlig verfehlt. Das wahre Problem ist: Die „Klimastrategie” ist viel zu konkret!

Es ist komplett unnötig, dass sich unsere Regierung Gedanken macht wie viele Ölheizungen es in Zukunft geben darf oder wie viele Solarpanels installiert werden müssen oder wie viele Elektroautos herumfahren sollen. Alles, was sie tun muss, ist eine Steuer für CO2-Emissionen einführen und dann dem Markt die Aufgabe überlassen herauszufinden, welche Heizungssysteme, welche Verkehrsmittel und welche Stromerzeugungsmethoden sinnvoll sind.

Natürlich gibt es wie bei jeder neuen Steuer administrative Herausforderungen: Wer genau soll die Steuer abführen? Wie genau wird die Steuer ermittelt? Wie geht man mit Importen und Exporten um? Aber ich bin mir sicher die braven Beamten des Finanzministeriums sind kreativ genug diese Probleme zu lösen, zumal sie auf die Hilfe von Umweltökonomen und Finanzwissenschaftlern zählen können. Schlaue Leute haben sich über all das schon Gedanken gemacht und Konzepte entwickelt. (Z.B. hier)

Es könnte so einfach sein.

]]>However, I recently stumbled across a “Treatise on Money“ by the 16th century Jesuit theologian Luis de Molina which contains, among other economic ideas, a concise statement of the quantity theory as well as some empirical evidence for it.

Molina is best known for coming up with a clever solution to the theological problem of reconciling the omniscience of God with the free will of humans: God, Molina reasoned, knows exactly how humans would behave in any given hypothetical situation (this kind of knowledge Molina called *scientia media*, „middle knowledge“). In other words, God is the perfect economist: He has complete knowledge of all His creatures’ preferences, their beliefs and their cognitive biases, and therefore can predict what choices they will make freely when faced with any possible budget constraint. This idea helps solving a number of important theological problems, like the issue of predestination or the theodicy.

Anyway, Molina was not only a great theologian, but also a superb economist. For instance, he clearly understood the logic of supply and demand in determining market prices and also saw the logic of no-arbitrage conditions. And here is his explanation of differing price levels in different places:

There is another way that money may have more value in one place than in another: namely, when it is more abundant. In equal circumstances, the more abundant money is in one place so much less is its value to buy things with, or to acquire things that are not money. Just as the abundance of merchandise reduces their price when the amount of money and quantity of merchants remains invariable, so too the abundance of money makes prices rise when the amount of merchandise and number of merchants remain invariable, to the point where the same money loses purchasing power.

And here is his evidence for the theory:

]]>So we see that, in the present day, money is worth in the Spanish territories much less than what it was worth eighty years ago, due to the abundance of it. What was bought before for two today is bought for five, or for six, or maybe for more. In the same proportion has the price of salaries risen, as well as dowries and the value of real estate, revenues, benefices, and all other things. That is exactly why we see that money is worth much less in the New World, especially in Peru, than in the Spanish territories, due to the abundance there is of it. And wherever money is less abundant than in the Spanish territories, it is worth more. Neither is it worth the same in all parts because of this reason, yet it varies according to its abundance and all other circumstances. And this value does not remain unaltered as if it were indivisible, yet fluctuates within the limits defined by the people’s estimation, the same as happens with merchandise not appraised by law. This money’s value is not the same in all parts of the Spanish territories, but different, as ordinarily it is worth less in Seville—where the ships from the New World arrive, and where for that reason there is usually abundance of it—than what it is worth in other places of the same Spanish territories.

Well, the new Austrian minister of finance just held his budget speech, in which he announced a zero budget deficit in the coming years. Assuming the government follows through on this plans, this would indeed bring down the debt-to-GDP ratio to 62 percent, exactly as our main projection predicted.

Here is the finance ministry’s proposed budget path:

And here our main projection from the paper (note that the initial debt level is slightly lower due to different definitions of public debt; the dark and light blue areas indicate the 75 and 95 percent probability bands around the median, which is in black):

Ladies and Gentlemen, this is what a perfection prediction looks like.

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The license plate celebrates the 200th birthday of the State of Indiana in 2016. 200 years! This means, in a sense, Indiana is older than many of the states of the European Union. In 1816, Germany was still a patchwork of small territories, loosely connected through the German Confederation – of which Austria was a part. Italy was merely a geographical description – the process of Italian unification had not even begun. Greece was just a province of the Ottoman empire. Belgium, until 1815 known as „Austrian Netherlands“, was part of the United Kingdom of the Netherlands. France did exist as a nation then, however, while the people of Indiana lived for 200 years under the same political system and only once made marginal changes to their constitution (more about this below!), the French during the same time went from the post-Napoleonic Bourbon monarchy to the Second Republic to the Second Empire, then back to the Third Republic, then to totalitarian rule under the Nazis, and finally back to Fourth and now the Fifth Republic. As far as I am aware, there is no European country which has had the same constitution for the past 200 years without interruptions or major changes – the single exception I can think of is the United Kingdom which always had the same constitution: none.

There is another striking fact about the history of Indiana. Indiana has been in a monetary union with the rest of the United States for as long as it existed. And during its early history, it has had its own debt crisis which bears a striking resemblance to the recent history of the much younger European monetary union.

When Indiana became a State in 1816, it was mostly a wilderness at the margin of civilization. The only major road in the country was the Buffalo Trace – literally a trace created by migrating bison herds. Population was only 65,000 initially, but growing fast. The government of the young state decided to take the country’s infrastructure into the 19th century. And 19th century infrastructure, they figured, was going to be canals. So, they launched a giant public investment program, called the Mammoth Internal Improvement Act, spending 10 million dollars (equivalent to 260 million current dollars, roughly 100% of GDP at the time) on canals and toll roads. The heart of the project was the Wabash & Erie Canal connecting the Great Lakes with the Ohio River. „Crossroads of America“ was the official state motto of Indiana.

To finance these projects, the governor of Indiana, a certain Noah Noble, had a plan: some money was to be raised by selling public lands, some by raising taxes, and some by borrowing from the Bank of Indiana, which was partly state-owned. The Bank of Indiana refinanced itself by issuing bonds, backed by the state, at the London exchange.

Initially, the plan looked like a big success. The construction works employed many thousands of people and provided a stimulus for the economy. Borrowing costs were low and spirits were high. But soon, problems started to appear. It turned out that the government had greatly underestimated the costs of building the canals, mostly because they failed to take into account the damage done by muskrats who burrowed through the walls of the dams. Critical voices in the State Congress regarded the canals as a total waste of money. Railroads, they argued, were the future! Nobody seemed to listen.

And then, in 1837, a financial crisis broke out. The crisis was triggered by the Bank of England which, in an attempt to curb the outflow of gold and silver reserves, raised interest rates. This had a direct impact on Indiana whose borrowing costs skyrocketed. It also had an indirect effect: since the United States was on a gold and silver standard, American banks were forced to follow the Bank of England in raising interest rates, which led to a credit crunch and a nation-wide recession. (A classic example of a monetary policy spillover effect!)

The combination of stagnant tax revenues, exploding construction costs and rising interest rates meant that State of Indiana was effectively bankrupt at the end of 1841. So they sent the head of the Bank of Indiana to London to negotiate a restructuring of the debt. The creditors agreed to a haircut of 50% of the debt. In exchange, Indiana handed over control of most of the canals and roads, many of them still unfinished. The Wabash and Erie Canal was held in trust to pay off the remaining debt. It operated until the 1870s yielding a low profit, but was soon made obsolete by – the railroads which turned out to be the key infrastructure of the 19th century.

The conclusion Indiana drew from this was that the long-run costs of government borrowing far exceed the short-run benefits. Which is why in 1851, they adopted an amendment to their constitution, forbidding the State government to get into debt (except in cases of emergency).

I’d say there is a thing or two our modern European states can learn from this story.

]]>In this post I want to ask the question whether this threat is a credible one. I will have two answers to this question. Yes and no.

Haha. Well, it depends on what you call a “credible” threat. The most commonly known notion of a non-credible threat is due to Reinhard Selten. Paraphrasing his work somewhat, a threat is not credible if, once asked to actually go through with it, people do not find it in their own interest to do so. Reinhard Selten then defined a Nash equilibrium to be free of non-credible threats if it is a subgame perfect equilibrium, that is a Nash equilibrium that is also a Nash equilibrium in every subgame. What does that mean? Well this means the strategy profile that both players in the game play is such that **no matter what has happened in the game so far** the strategy profile from any point onwards is still so that no player would want to deviate from it if they believe the other player to follow their part of this strategy profile.

Let us come back to the nappy-changing game as described in my first post in this series. Here is a brief summary of this game. I ask Oscar if his nappy is full (after some initial but uncertain evidence pointing slightly in this direction). Oscar can make his answer depend on the true state of his nappy (full or clean) and this answer can either be “yes” or “no”. I then listen to his answer and make my decision whether to check the state of his nappy or not a function of what answer he gave. Let me reproduce the normal form depiction of this game again here:

The one-shot game only has equilibria in which I do not trust Oscar’s statement and always check his nappy. This is bad for both of us. It would be better for both of us if Oscar was truthful and I believed him. This, I then argued in the previous post in this series can be made an equilibrium outcome if the two players play the grim trigger strategy as suggested by all these proverbs. Note that I keep assuming that I (as a player in this game) can always find out about the true state of the nappy sooner or later, an assumption that has rightly been pointed out not to be completely plausible in all cases. [One could here talk about the more recent literature on repeated games with imperfect monitoring, but I will refrain from doing so at this point – the reader may want to consult the 2006 book by Mailath and Samuelson on Repeated Games and Reputations]

The grim trigger strategy is as follows. I believe Oscar as long as he was always truthful in the past (and as long as I was always trusting in the past). Once I catch Oscar lying (or once I have not trusted Oscar) I never again believe him and always check his nappy from then on. Oscar is truthful as long I have always trusted him (and as long as he has always been truthful). Once he catches me not trusting him (or once Oscar himself was untruthful) Oscar will always so no from that point on. The statements in brackets probably seem strange to someone not used to game theory, but they are needed for the statements below to be fully correct.

This grim trigger strategy, then, is a subgame perfect equilibrium, provided Oscar’s discount factor . Why? I have already argued that, in this case, Oscar would not want to deviate from the equilibrium path of being truthful, because lying would lead to my never trusting him again and this is sufficiently bad for him if his discount factor is sufficiently high. I certainly have no incentive to deviate from this equilibrium path, because I get the best payoff I can possibly get in this game. But subgame perfection also requires that the threat, when we are asked to carry it out, is in itself also equilibrium play. So suppose Oscar did lie at some point and I (and Oscar) are now supposed to carry out the threat. What do we do? Well, we now play the equilibrium of the one-shot game forever and ever. But this is of course an equilibrium of the repeated game, so the grim trigger strategy described here does indeed constitute a subgame perfect equilibrium.

So according to Reinhard Selten’s definition the punishment of never ever believing Oscar again is a credible threat.

But others have argued that Reinhard Selten’s notion of a credible threat is only a minimal requirement and further requirements may be needed in some cases. I do not know what Reinhard Selten thought of this, but I guess he would have agreed. So what is the issue?

Oscar and I when we look at this game should realize that we would both like to play the truthful and trusting equilibrium path. To incentivize us to do so, especially Oscar in this case, we need to use this threat of me never again believing him if I catch Oscar lying. But suppose we are in a situation in which I have to carry out this threat. Then we would both agree that we are in a bad equilibrium and that we would want to get away from it again. In other words we both would want to renegotiate again. But if Oscar foresees this, that I would always be willing to renegotiate back to the truthful and trusting outcome of the game, then his incentives to be truthful are greatly diminished.

With something like this in mind Farrell and Maskin (1989) and others have put forward different versions of equilibria of repeated games that are **renegotiation-proof**, that is immune to renegotiation.

They call a strategy profile of a repeated game a **weakly renegotiation proof** equilibrium if the set of all possible prescribed strategy profiles (after any potential history) are Nash equilibria in the subgame and cannot be Pareto-ranked. This means that for any two possible prescribed strategy profiles (or continuation equilibria as they call it) must be such that one person prefers one of the two while the other person prefers the other. Note that this is not the case in the grim trigger equilibrium of the repeated nappy changing game. In this subgame perfect equilibrium both Oscar and I prefer the original equilibrium of the game over the one carried out after Oscar is lying.

So what is weakly renegotiation proof in the repeated nappy-changing game? Well, I have made some calculations and the best weakly renegotiation proof equilibrium for me (in terms of my payoffs) that I could find is this: On the equilibrium path Oscar is truthful and I randomize between trusting Oscar with a probability of and with a probability of I play “do not check (regardless of what Oscar says)”. For this to work I have to randomize using dice or something like this in such a way that Oscar can verify that I correctly randomize. If Oscar ever deviated I then verifiably (to Oscar) randomize by playing “check nappy regardless of Oscar’s answer” with a probability of and trusting Oscar with a probability of . Oscar then continues to be truthful. Oscar incentivizes me to behave in this way (after all I am letting Oscar do what he wants sometimes, which is not what I would want) by punishing me, if I ever deviate, with the following strategy. He would continue to be truthful but ask me to play “do not check (regardless of what Oscar says)”. This complicated “construction” works only if the punishment is not done forever, but only for a suitably long time after which we go back to the start of the game with the equilibrium path behavior. Whenever one of us deviates from the prescribed behavior in any stage we simply restart the punishment phase for this player.

This probably all sounds like gobble-dee-gook and I admit it is a bit complicated. Before I provide my final verdict of this post let me just clarify this supposedly best-for-me renegotiation proof equilibrium. Suppose is essentially one half. Then in the prescribed strategy profile, on the equilibrium path, I am randomizing between trusting Oscar (which I find best given that he is truthful) with a probability of 2/3, that means two thirds of the time. But one third of the time I leave Oscar in peace even when he tells me his nappy is full. As this happens one half of the time I actually leave him in peace despite a full nappy in one sixth of all cases. I have to do this in order for my punishment of him to be actually preferred by me over the equilibrium path play. In the punishment I mostly switch probability from leaving Oscar in peace to checking him always, which is something that I do not find so bad, but that Oscar really dislikes.

Well, I do not know if you find this very convincing, but I do think that the grim trigger strategy is not really feasible when it comes to teaching kids not to lie. What I actually use in real life is a simple trick. I do not punish behavior only within the nappy-changing game itself. I use television watching rights, something outside the game I just described. The great thing about this is that while Oscar does not like it when his television time is reduced I am actually quite happy when he watches less television and so this works as a renegotiation proof punishment. But the fact that I do this can be explained by the failure of the grim trigger strategy to be renegotiation proof.

]]>The nappy-changing game as I have written it down in my post on lying (which you may need to read before you can read this post) can also be seen as the game between the boy and his elders. There are two states of nature. Either there is a wolf or there is not. The boy, who is watching the sheep, knows which state it is and the elders, who are somewhere else, do not. The boy has four (pure) strategies: never say anything, be honest (cry wolf when there is one, be quiet when there is none), use “opposite speak”, and always cry wolf. The elders who listen to the boy’s cry also have four (pure) strategies: always come running, trust the boy, understand the boy as if he was using opposite speak, and never come running. Supposedly, the elder’s preferences are just as mine are in the nappy-changing game. They would like to come running if there is a wolf, and they would like to keep doing whatever it is they are doing when there is no wolf. The boy’s preferences seem to be the same as Oscar’s in the nappy-changing game. If there is a wolf the boy would like to see his elders to come running to help, but the boy would like the elders to come running even when there is no wolf (he gets bored I suppose). The one slight difference between the two games seems to be that the assumed commonly known probability of a wolf appearing, is now less than a half (if we assume that the payoffs are still just ones and zeros). Well, what matters is that the ex-ante expected payoff of coming running is lower than the ex-ante expected payoff of staying put. We infer this from the elders’ supposed actions of staying where they are when they do not believe that there is a wolf. If the elders had found a wolf attack really disastrous and at the same time sufficiently likely, then after finding the boy not trustworthy, they would have decided to come always, that is to watch out for wolves themselves. The fact that they let the boy do the watching (and to then ignore his warnings – because they do not believe him) tells us that without further information about the likelihood of the presence of a wolf, they prefer to stay where they are (probably doing something important) and risk losing one sheep to a wolf over keeping constant watch for wolves.

In any case the same model as the nappy-changing game, but now with , now takes account of the supposed (long-run) behavior in this story. The game still has only two pure equilibria and they involve the boy either crying wolf in both states (or not doing so in both states), but now with the effect that the elders never come.

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