# A quick game theoretic thought about the Brexit negotiations

In the last few days, I watched the British news a bit about Boris Johnson forming the new UK government. There was of course a lot of talk about the Brexit negotiations. I was a bit puzzled at one point about some of Boris Johnson’s statements. On the one hand there is a lot of talk about being prepared for a hard Brexit and on the other I also heard him say something like that “the chance of a hard Brexit is one in a million” a little while back. So why prepare for some contingency that you do not expect to happen under essentially any circumstances? Also you get the feeling that Boris Johnson, despite having said that, would not so much mind a hard Brexit. In this short post, I explore why all this might actually all make good game theoretic sense (and why perhaps, at least for this matter, his UK opponents should get on board with his strategy if they care about the UK unless, of course, they think they can still stop Brexit).

# 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?

# The game theory of everyday life – the secret handshake

You are visiting another university and have arranged to meet someone from that university in the lobby of the hotel you are staying at. The hotel lobby is busy with many people and (for some strange reason) neither you nor the person you are supposed to meet have recognizable pictures on their webpages. How will you find each other? What is the mechanism behind it? How is this possible at all?

# The game theory of everyday life – where to stand in a lift

When you enter a lift, a bus, a doctor’s waiting room, or any other smallish place in which you and others are just waiting for something to happen, one of the key decisions you face is to choose where to stand or sit. How do we do this? What are the key factors (motives) behind our decisions? What are the consequences of this? What are the testable implications?

# 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?

# The game theory of everyday life – pedestrian traffic

Our starting point is Goffman’s Relations in Public Chapter 1.II on “Vehicular Units”. Goffman is here interested in the norms that regulate traffic, especially but not only pedestrian traffic. He first quotes Edward Alsworth Ross, Social Control, New York: The Macmillan Company (1908), page 1: “A condition of order at the junction of crowded city thoroughfares implies primarily an absence of collisions between men or vehicles that interfere one with another.”

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.

# The game theory of everyday life inspired by the work of Erving Goffman – Introduction

In April 2018 I spent a week at the Research Center for Social Complexity (CICS in Spanish) at the Universidad del Desarrollo (UDD) teaching a PhD research course on game theoretic modelling. The idea of this course, developed together with Carlos Rodriguez-Sickert, was to make it an experiential course of model building from question to model. We would start by reading parts of chapters of two books by Erving Goffman that deal with how people interact in public places and then attempt to provide game theoretic models of what we read.

# On Lying, III

In my previous post I argued that a person can be kept truthful (in a repeated setting) by the threat of never believing this person again once this person has been caught lying even once. This is a strategy that, as I have pointed out in my previous post and in one comment, many proverbs suggest.

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.   Continue reading

# A side remark on lying: the boy who cried wolf

You probably know the story of the boy who cried wolf. A boy is charged by his elders to watch their flock of sheep and to call them as soon as he sees a wolf approaching. The wolf supposedly would want to kill one of the sheep, and the boy’s cry of “wolf” would bring the elders running to fend of the wolf to protect their sheep. In the story the boy on two occasions cries wolf when there is no wolf, with the effect that the elders come running both times and being very upset at his “lying” (and the boy pleased). But when he does cry wolf for a third time, this time when there actually is a wolf, the elders do not believe him and stay away. This, of course, has the disastrous (?) effect that the wolf kills one of the sheep.

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, $\alpha$ 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 $\alpha < \frac12$, 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.

# On Lying, II

There is a German saying about lying: “Wer einmal lügt, dem glaubt man nicht, und wenn er auch die Wahrheit spricht.” The closest corresponding idiom in English is probably this: “A liar is not believed even when he speaks the truth.” This is good enough for the moment but there is a little bit more information in the German saying than in the English one and this little bit more will become interesting in my discussion further below.