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.

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.

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