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?
I just read an article on the bbc about sports data company gracenote’s estimates of countries’ winning probabilities for the upcoming soccer world cup. I then looked up the best current betting odds on oddschecker. These are, of course, subject to change. I looked at them on the morning (Pacific Time) of the 7th of June.
I then looked at the expected return to a one Euro bet on the various countries winning the world cup under the assumption that gracenote’s estimates are completely correct. So if you believe in gracenote’s estimates as the abolute truth, what should you bet on?
Well, Brazil is the favorite according to gracenote but also in the betting odds. Gracenote gives them a 21% chance of winning the world cup, and at current best odds of 9:2 you would win 4,50 Euros if you put 1 Euro on Brazil. This means you would expect to get 4,5 * 0,21 = 0,945 Euros back. So if you are risk averse or risk neutral you should not bet on Brazil at these odds, but if you had to you could put a Euro on Brazil. Germany has similar best odds of 5:1, but gracenote does not rate them so highly, giving Germany only an 8% chance of winning. So you would only expect to win back 5*0,08=0,40 Euros for every Euro you place on Germany. This means that, if you could, you should “short sell” Germany to make money in expectation. This is not so easy to do in sports betting markets so let’s not pursue this here. It turns out that most of the better teams are not rated as highly by gracenote as they are in the betting odds.
So, again, what should you bet on if you believe in gracenote’s estimates? According to gracenote Peru has a 5% chance of winning the world cup. At current odds of 325:1 you would get an expected payout of 325*0,05=16,25 Euros for every Euro you put on them. This is an expected return better than anything you can get on the stock market I would guess. Mexico, Switzerland, Colombia (with expected payout of 3,75, 3,50, and 2,60 Euros for every Euro you put on them) are also high return bets.
I am afraid, though, that I believe in the efficiency of sport betting markets much more than in one sports data company’s estimates, so I will not follow these suggestions myself. If you want to know more about the efficiency or inefficiency of betting markets a good starting point would be a 1988 survey by Thaler and Ziemba.
One day later, on the 8th of June, I noticed that Peru’s odds have gone down to 200:1. Perhaps this was a reaction to the new information provided by gracenote (although I am not quite sure when their estimates were posted). You would, however, still make an expected winning of 200*0,05 = 10 Euros for every Euro you put on Peru if you believe gracenote’s estimates.
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.