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When Equality Trumps Reciprocity

The largest contribution of this strain of modeling comes not from the assumption of boundedly rational agents, but rather the careful investigation of the effects of particular social structures on the equilibrium outcomes of various games. Much of the previous literature on evolutionary games has focused on the assumptions of infinite populations of agents playing games against randomly-assigned partners. Skyrms and Alexander both rightly emphasize the importance of structured interaction. As it is difficult to uncover and represent real-world network structures, both tend to rely on examining different classes of networks that have different properties, and from there investigate the robustness of particular norms against these alternative network structures. Alexander (2007) in particular has done a very careful study of the different classical network structures, where he examines lattices, small world networks, bounded degree networks, and dynamic networks for each game and learning rule he considers. A final feature of Skyrms and Alexander’s work is a refinement on this structural approach: they separate out two different kinds of networks. First, there is the interaction network, which represents the set of agents that any given agent can actively play a game with. Second is the update network, which is the set of agents that an agent can “see” when applying her learning rule. The interaction network is thus one’s immediate community, whereas the update network is all that the agent can see. To see why this is useful, we can imagine a case not too different from how we live, in which there is a fairly limited set of other people we may interact with, but thanks to a plethora of media options, we can see much more widely how others might act. This kind of situation can only be represented by clearly separating the two networks.

Thus, what makes the theory of norm emergence of Skyrms and Alexander so interesting is its enriching the set of idealizations that one must make in building a model. The addition of structured interaction and structured updates to a model of norm emergence can help make clear how certain kinds of norms tend to emerge in certain kinds of situation and not others, which is difficult or impossible to capture in random interaction models.