Coordination Concepts

The concept of coordinated group behavior has received great attention in the analysis of social systems (cf. Schelling (1960), Lewis (1969), Bicchieri (1993), Cooper (1999), Malone et al. (2003), Goyal (2007), Jackson (2008), Shoham and Leyton-Brown (2009), Easley and Kleinberg (2010)). Much of the focus is on so-called coordination games, where two or more individuals must each choose one of several alternative actions. Most such studies, however, do not involve explicit notions of group-level behavior. Rather, a social engagement is deemed to be a coordination scenario if there is an opportunity for the individuals to cooperate for their mutual benefit. Games such as Hi-Lo, the Battle of the Sexes, and the Prisoner's Dilemma as discussed by Axelrod (1984) are prime examples of coordination scenarios. Mutual benefit, however, is not the same as group preference. There is a difference between the behavior of individuals whose categorical preferences just happen to be aligned, even though there is no explicit social relationship between them, and the behavior of individuals who are linked together by social influence. With the former, any notions of group benefit are exogenously imposed ex post, but with the latter, group preference, if it exists, emerges endogenously as a consequence of the social relationships that are formed as ex ante social influence propagates through the network.

If all individuals possess categorical preferences, then the concept of group preference is not an innate property of the collective. It is an uncomfortable fact that game theory does not provide a definitive resolution of the so-called cooperative scenarios such as Hi-Lo and the Battle of the Sexes. Both games have multiple Nash equilibria, but game theory does not provide a definitive way to choose from among them.