What are the contexts that give rise to cooperation as opposed to conflict? When should we love thy neighbor, turn the other cheek, or escalate? Game theory is an effort to formalize this problem such that we can ask what decisions we should make when the consequences of those decisions depend on the decisions of others. By this accounting, war is a game, as is negotiation, rock-paper-scissors, and love making. The difference is in the payoffs. Being rational is about making decisions that lead to the best outcomes. The hawks and doves of political foreign policy – who advocate for more or less aggressive military intervention – are rational beings in this world, because the nature of the payoffs demands certain kinds of responses. The pragmatics of high stakes games underpin quotes like John F. Kennedy’s "We can secure peace only by preparing for war." But is Kennedy’s statement rational by the logic of the game in which it is embedded? Is it rational when games of conflict are played repeatedly in a network of global interactions? By combining game theory with network science, we can make some progress toward understanding these issues.

By looking at networks as collections of smaller elementary structural forms – mainly all combinations of two nodes (dyads) and three nodes (triads) among whom ties may or may not exist – one can learn much about the larger structure. This is especially useful when that structure is very large and therefore difficult to see as a whole. And yet, these most elementary forms of social structure are not simply mathematical constructs; they reflect the fundamental ways that social actors relate with one another as individuals and as social units (i.e., sociality). Thus, a network with many social elements of one type, and fewer of another, suggests a certain way of relating involved in how the network has formed and where it might be going. In this chapter, we introduce the reader to dyads and triads as forms of interacting and relating. We cover techniques for decomposing networks into these constituent elements and connecting variation at the micro level as a way of seeing macro-level structures.

The concept of a “focus of activity” was developed to describe the nature of non-network social structures that often underly the formation of intersecting clusters of ties in large-scale social networks. The primary purpose of the “focus theory” was to encourage network analysts to consider the impact of those underlying structures before attributing too much of the structure and consequences of social networks to psychological processes, individual choices, or self-contained network processes. We have been pleased to see that network researchers have increasingly considered the impacts of these non-network social structures. Nevertheless, we take this opportunity to clarify and extend the focus theory in ways that may make it more applicable and useful for more purposes. We show how the focus theory can be reconciled with some influential network theories that may initially appear inconsistent with it. We discuss how the focused organization facilitates indirect connections across large-scale social networks; and, we explicitly extend the focus theory by considering additional processes causing both the loss of old ties and the accumulation of new ties within clusters over time.

Humans are the end point of almost four billion years of evolution. The generally accepted explanatory theory is Charles Darwin’s theory of evolution through natural selection, brought on by a struggle for existence. Darwin bolstered his case through a “consilience of inductions,” showing how evolution through selection explained in many areas right across the life sciences – behavior, fossil record, geographical distributions, morphology, taxonomy, and embryology. The missing element was an adequate theory of heredity, supplied by the Moravian monk Gregor Mendel. A major problem was why random change in the units of heredity, mutations of the genes, should provide enough suitable material for selection to work on. Theodosius Dobzhansky solved this problem by hypothesizing that all populations contain much variation, quite enough for selection to work on. His student, Richard Lewontin, using molecular techniques – gel electrophoresis – showed that Dobzhansky’s hypothesis was right.