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).
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?
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?
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?
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?
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.
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.