Economics on the beach V: on towels, parking spots, and job protection

You just arrived at your dream summer resort. You had a restful night almost entirely uninterrupted by mosquitoes. You just woke up and had a leisurely and plentiful breakfast. You are making your way to the swimming pool that looked so enticing on the webpage. And what do you find? You find towels. In fact you find towels on every single one of the lounge chairs that the resort has provided. While almost no lounge chair is actually occupied, not a single lounge chair is really available. Economics is supposedly (primarily?) about the allocation of scarce resources. So what about the scarce resource that is a lounge chair next to the pool in a holiday resort?

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The game theory of everyday life – gallantry

Chapter 1.II on “Vehicular Units” of Goffman’s Relations in Public has many more “nuggets” that are amenable to a game theoretic analysis in addition to the one I described in my previous post. In footnote 23 on page 17, for instance, he talks about what we would call “common knowledge” and that eye contact is perhaps the only way to establish it (referring here to the earlier work by Lewis 1969, Scheff 1967, and Schelling 1960). This could lead one to discuss Ariel Rubinstein’s “email game” (1989, ECMA) and some of the literature thereafter (and before). On page 14, Goffman talks about “gamesmanship” in whether or not we let others “catch our eye”. I would like to think here about pedestrians visibly (to all who do not do the same) refusing to “scan” their environment by looking at their smartphone while walking. This would lead me to discuss a paper of Hurkens and Schlag (2002, IJGT) and possibly beyond that. There is also Goffman’s discussion of the apparently commonly observed practice of the “interweaving” of cars when they have to go from two lanes into one. I have not yet seen a game theoretic treatment of this phenomenon and I am not quite sure (at the moment) how one would explain it.

But in this post I want to take up Goffman’s brief mention (on pages 14-15) of special circumstances that seem to necessarily lead to what he calls “gallantry”. This is when a path that pedestrians take in both directions at some point becomes too narrow for two people to pass simultaneously. Then one has to wait to let the other person pass. But who should wait and who should be first to pass?

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Me, Myself and Economics: Disequilibrium

I considered to choose ‘A Non-Equilibrium Approach’ as a subtitle of my dissertation thesis. About at the same time a colleague of mine stated that ‘disequilibrium economics’ are a ‘logic implausibility’ as an equilibrium in economics is not much more than a consistency condition – different to the notion in physics where it mainly refers to a state where the described system is at rest. I have to disagree with this maybe unintentional attempt to whitewash a bunch of approaches which are – as probably every other approach – criticized for good reason.

Just think of basic micro or macro and the definition of a market or an economy in equilibrium. There the term is not used to describe consistency in the derivation of the outcome, but mainly refers its characteristics – for example that supply and demand are balanced. Go further in the curriculum and think of an equilibrium in game theory. While it is also derived in a way which is consistent with the stated assumptions, its description states more than that – for example that it is a combination of strategies for which no individual has an incentive to unilaterally deviate.

Therefore, equilibrium approaches in my opinion go beyond detecting an outcome that is logically implied by assumptions and step-by-step analytics. They also tend to presume an outcome of a certain type and thereby risk the neglect of other outcomes, strategies, behaviour, and thereby even whole issues that may be highly relevant in reality.

In case my concern is not clear, a discussion of Rubinstein’s famous e-mail game may help. The e-mail game may be described as the following: A couple wants to meet and prefers being together over being separated. However, if it rains they prefer to meet inside, otherwise the prefer to meet outside. Whether it rains or not is determined by nature and only one person, let’s assume the woman, knows the weather for sure. If it will rain, she sends an e-mail to the man. Every received e-mail is read and automatically triggers a response, but every e-mail also gets lost with a certain small probability. That means that the e-mail conversation may last for a long time and even forever, but the probability for the latter case tends to be zero.

Because of the small but nevertheless positive probability for an e-mail to get lost, both parties will never know for sure how many e-mails have been sent. The woman knows whether she sent an e-mail or not, but she is confused about the state where one or two e-mails were sent (captured by the partition Pw). While it may be that the second e-mail – sent by automatic response from the man’s account – got lost, it also may be the case that her e-mail did not pass through in the first place. The moment the second e-mail passes through, the third e-mail is triggered automatically and she can distinguish that state from the ones before. However, she again cannot distinguish between the state of three and four e-mails sent – because if she would know about the fourth e-mail, she would have automatically sent the fifth, being in another state. The man faces a similar incompleteness of information (captured by the partition Pm). He in turn is confused about whether none or one e-mail was sent, just like he is confused about whether two or three e-mails were sent and so on.

Rubinstein thereby shows that the strictly formal approach does not lead to an equilibrium in which they meet outside in the nearby game even if there is a high probability for the information to pass on. In fact, the formal result of the game described above is that none of the two will risk to go outside as there is no state (described in terms of e-mails sent) about whose appearance exists common knowledge. However, the example not only shows how easy simple games may get complicated in formal term, but also shows how misleading the strictly formal conclusion can be with regard to an underlying issue. It was about a couple who wants to meet, inside on rainy days, outside otherwise. They both know their preferences. They differ only in the information they have – first about the state of nature and second about how many e-mails are sent. The second issue however should not be the one of primary interest. Instead a social scientist and therefore economist should just ask: how many e-mails have to be sent that they both know that they both know about the weather and therefore human beings of these days will coordinate for the preferred equilibrium.

One e-mail sent just states that it is rainy and the woman knows about it. Two e-mails sent means that the man received this important information, but the women does not know that yet. Three e-mails sent means that the woman knows that the man knows. Four e-mails sent means that the man now knows that the woman knows that he knows. Five e-mails mean that the woman now knows that the man knows that the women knows that the man knows. At the latest after the sixth and seventh e-mail both know that they reached the aspired situation where both know that they both know.

While they can never be sure that their last e-mail passed through, they reach a state where human beings of these and thereby the economic agents of interest will not care about it. Agents may differ with regard to the number of e-mails they require in order to believe in a successful coordination, but I claim that there are not much of them who require more than the five to seven e-mails.

So, while the formal equilibrium approach provides some insights in favour of a theoretical statement about mutual and common knowledge, it risks to draw too much attention towards the wrong issue or at least away from non-equilibrium outcomes that may be highly probable in reality. I think that this is a general issue of equilibrium economics, which are worthwhile and helpful in many regards, but always have to be done as well as interpreted with caution.

Disequilibrium economics is a logical impossibility

This is going to be super abstract, potentially infuriating and probably wrong.

I sometimes hear people talk about „disequilibrium economics“ and I think I know what they have in mind. Equilibrium is often associated with a system at rest. That’s the physicist’s notion of equilibrium: a ball sitting at the bottom of a bowl, a planet moving around the sun in a stable orbit, etc. Disequilibrium is something not at rest: you hit the ball and it jiggles around inside the bowl, a planet collides with another and flies off its orbit.

Economists have a different notion of equilibrium. Indeed, they have several different notions depending on the context. But basically, an economic equilibrium is a consistency condition imposed on a model by the economist. It follows that „disequilibrium economics“ is a logical impossibility.

Let me explain. Economists build models to explain certain real-world phenomena, say bank runs. Inside these models there are agents, e.g. savers, banks, firms, each described by their preferences, beliefs and constraints. For instance, a saver wants to keep her money in the bank as long as she believes she will get it back eventually. Whether she can get it back depends on the number of savers who demand their money back. As long as most of them don’t want to withdraw their money, everything is fine. However, if there is a critical mass of savers who want their money back, the bank needs to liquidate its assets prematurely at „fire-sale“ prices, which means it cannot repay all the savers’ deposits in full. You have two equilibria: one in which nobody runs on the banks, the banks carry their investments to maturity, everyone gets repaid; another one in which everyone runs, the banks liquidate their investments prematurely, people don’t get repaid in full.

Only the first of these equilibria can sensibly be characterized as „a system at rest“. In the second equilibrium, nothing is at rest: there is chaos in the streets, banks go bust and people get hurt.

What characterizes both equilibria are two conditions:

  1. Everyone is doing the right thing given their preferences, beliefs, and constraints. The saver who runs on the bank is doing the right thing: Given that everyone else runs, she should run, too, or else she will get nothing. This is called rational behavior, but it should really be called consistent behavior. It’s behavior that is consistent with an agent’s preferences, beliefs and constraints.
  2. Things need to add up. Or to put in fancier language: individual decisions need to be consistent with each other. The total value of deposits repaid cannot exceed the total value of assets held by the banks. If there are 10 cookies and I want to eat 8 and you want to eat 5, that’s not an equilibrium. It’s a „disequilibrium“. It’s a logical impossibility.

If you’re a behavioral economist, you may take issue with condition (1). You may argue that people often don’t do the right thing, they are confused about their beliefs and they don’t understand their constraints very well. That’s fine with me. Let agents do their behavioral thing and make mistakes. (Although you must be explicit about which mistake out of the approximately infinite number of mistakes they could make they actually do make.) But still, things need to add up. I may be mistaken to want 8 cookies and you may be confused to want 5, but there are still only 10 cookies. Behavioral economics still needs condition (2).

If you’re a first-year undergrad, you may think equilibrium means that markets clear. Then you learn about asymmetric information and realize that things like credit rationing can occur in equilibrium. And you learn about the search models. Adding up constraints may be inequality constraints.

Finally, you cannot „test for equilibrium“ with data. Equilibrium is that which your model predicts. If your prediction is contradicted by the data, it’s because your model is wrong, not because there is „disequilibrium“. I have heard econometricians talk about error correction models where they call the error correction term a measure of „disequilibrium“. What they mean by that is that their economic model can only explain the long-run relationship between variables (the cointegration part), from which there are unexplained short-run deviations. But that just means the model is wrong for these short-run movements.

Equilibrium means consistency at the individual and at the aggregate level. It doesn’t mean stable, it doesn’t mean perfect. In fact, it is completely devoid of empirical content in and of itself. It only becomes meaningful in the context of a concrete model. And without it, economic models wouldn’t make any sense.