Modelling conformity and stereotyping in social groups with correlated equilibrium

What is it about?

This paper has its origins with the question of how social norms can be modelled using game theory. If conformity to a social norm is consistent with individual rationality then it should be an equilibrium of some underlying game. The issue is how exactly to capture that. Previous work has equated social norms with a Nash equilibrium in which similar people do similar things. We argue, however, that view is too constraining because many social norms involve similar people doing different things. For instance, the social norm of 'women stay at home and look after the children when men go out and work' requires husband and wife to do different things. To capture the possibility that people can conform to the same norm and yet perform different actions we use the notion of correlated equilibrium. The basic idea here is that behaviour is made conditional on signals, such as gender. It may well be that the signals are completely irrelevant to the task at hand, but they are a useful way to coordinate actions within the group or society. This way we can end up with an equilibrium where everyone uses the strategy 'if my role is x do x'. That everyone uses the same strategy captures conformity while roles allow for diversity in behaviour across the group. We show that a correlated equilibrium satisfying behavioural conformity exists very generally in games. We then apply our model to look at stereotyping. There are two sides to this issue. On the one hand we show that someone who stereotypes does not lose much by stereotyping. This is consistent with the general notion that stereotyping can be a useful way to reduce the informational costs of treating everyone as an individual. On the flip side we show that those who are stereotyped can lose significantly because of the stereotyping. This is consistent with the general notion that stereotyping can be harmful.

Featured Image

Why is it important?

Game theory may not seem the most obvious tool with which to model social norms and conformity. Game theory, though, can give critical insight on how social norms work and the kind of structure they can have. Our paper offers novel insight by connecting social norms with correlated equilibrium. This allows for a natural way to model roles within a group or society and then to bring in issues like stereotyping and prejudice. One limitation of our approach is that it is static. Future work will, hopefully, shed light on how norms evolve and roles come to be fixed in the first place.